This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 10 Vector Algebra – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 10 Vector Algebra Quiz 1 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Assertion:Two vectors in three dimensional space will always be coplanar.Reason:Vectors are free vectors with fixed magnitude and direction. A) Assertion and Reason are correct and reason is correct explanation. B) Assertion and Reason are correct but reason is not correct explanation. C) Assertion true reason false. D) Assertion false reason true. Show Answer Correct Answer: A) Assertion and Reason are correct and reason is correct explanation. 2. What is the formula for the section formula when the point is internally divided? A) R = (mb-na) / (m-n). B) R = (ma-nb) / (m-n). C) R = (mb + na) / (m + n). D) R = (ma + nb) / (m + n). Show Answer Correct Answer: C) R = (mb + na) / (m + n). 3. Sea $\vec v=\langle-6, -6\rangle$ A) $270^\circ$. B) $225^\circ$. C) $180^\circ$. D) $135^\circ$. Show Answer Correct Answer: B) $225^\circ$. 4. What is the result of the scalar product of two perpendicular vectors? A) 1. B) 0. C) -1. D) Undefined. Show Answer Correct Answer: B) 0. 5. Which of the following is true about the addition of vectors? A) It is associative. B) Both A and B. C) It is commutative. D) None of the above. Show Answer Correct Answer: B) Both A and B. 6. Given u = <3, 7> and v =<-5, 4>, find 2v-3u A) <-15, 3>. B) <-19, -13>. C) 23. D) <21, 2>. Show Answer Correct Answer: B) <-19, -13>. 7. Find the magnitude of the vector <-5, 12> A) 10.91. B) 13. C) 17. D) 7. Show Answer Correct Answer: B) 13. 8. If Tr(A) = 2+i then Tr[(2-i)A] = A) $3$. B) $2+i$. C) $2-i$. D) $5$. Show Answer Correct Answer: D) $5$. 9. What type of quantity is Work Done? A) Scalar. B) Vector. C) Depends on its usage. D) None of these. Show Answer Correct Answer: A) Scalar. 10. Given the vector v = 3i-2j +6 k, the magnitude of a is: A) 49. B) 6. C) 7. D) 36. Show Answer Correct Answer: C) 7. 11. What is the term for the angle between two vectors when their dot product is zero? A) Right Angle. B) Acute Angle. C) Obtuse Angle. D) Straight Angle. Show Answer Correct Answer: A) Right Angle. 12. Which of the following is an example of scalar magnitude? A) Force. B) Acceleration. C) Mass. D) Velocity. Show Answer Correct Answer: C) Mass. 13. Example for magnetic material used in data storage devices A) 45 Permalloy. B) CrO2. C) Cunife. D) Alnico. Show Answer Correct Answer: B) CrO2. 14. How do you know if two vectors are orthogonal? A) Their sum is 0. B) The angle between them is 0$^\circ$. C) The dot product is 1. D) The dot product is 0. Show Answer Correct Answer: D) The dot product is 0. 15. Given vectors PQ= 3i-2j and RQ=-2i+3j find PR A) 5i+5j. B) -5i+5j. C) -5i-5j. D) 5i-5j. Show Answer Correct Answer: D) 5i-5j. 16. Two vectors with same origin is called A) Collinear vectors. B) Coinitial vectors. C) Unit vectors. D) None of the above. Show Answer Correct Answer: B) Coinitial vectors. 17. A Vector is a tensor of Rank ..... A) 0. B) 1. C) 3. D) 2. Show Answer Correct Answer: B) 1. 18. Cross product of two vector always gives scalar quantity A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 19. Which of the following vectors is a unit vector? A) Vector with magnitude 3. B) Vector with magnitude 0. C) Vector with magnitude 1. D) Vector with magnitude 2. Show Answer Correct Answer: C) Vector with magnitude 1. 20. A resultant vector is A) Equal to the sum of one vector. B) Equal to the sum of two or more vectors. C) Equal to the difference of one vector. D) None of the above. Show Answer Correct Answer: B) Equal to the sum of two or more vectors. 21. Vector 2i-3j-2k and vector-2i+3j+2k are given, which is wrong for them? A) Equal vector. B) Co negative vector. C) Co initial vector. D) Collinear vector. Show Answer Correct Answer: A) Equal vector. 22. Magnetic permeability has units as A) A / m. B) Wb / A.m. C) Wb / m$^{2}$. D) Tesla / m. Show Answer Correct Answer: B) Wb / A.m. 23. What is the result of adding two vectors A and B using the triangle law of vector addition? A) A / B. B) A * B. C) A-B. D) A + B. Show Answer Correct Answer: D) A + B. 24. Given v = 6j, find 4v. A) 10j. B) 24j. C) 24i. D) 16i. Show Answer Correct Answer: B) 24j. 25. U=<4, 2>, v=<7, 1> . Find 2u-3v A) <21, 3>. B) <3, -1>. C) <-13, 1>. D) <-29, 7>. Show Answer Correct Answer: C) <-13, 1>. 26. The vectors 2i-3j + 4k and-4i + 6j-8k are collinear A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 27. What is the term for a vector whose initial and terminal points coincide? A) Unit Vector. B) Zero Vector. C) Collinear Vector. D) Position Vector. Show Answer Correct Answer: B) Zero Vector. 28. The scalar projection of vector u=(-7, 4) onto vector v=(4, -3) is A) -8. B) -16. C) 8. D) 40. Show Answer Correct Answer: C) 8. 29. What is the result of subtracting two vectors? A) Result of subtracting two vectors is the multiplication of the two vectors. B) Result of subtracting two vectors is the first vector minus the second vector. C) Result of subtracting two vectors is the sum of the two vectors. D) Result of subtracting two vectors is the second vector minus the first vector. Show Answer Correct Answer: B) Result of subtracting two vectors is the first vector minus the second vector. 30. What is a quantity that has only magnitude called? A) Force. B) Scalar. C) Direction. D) Vector. Show Answer Correct Answer: B) Scalar. 31. Sea $\vec v=\langle 0, -7\rangle$ A) $90^\circ$. B) $180^\circ$. C) $270^\circ$. D) $0^\circ$. Show Answer Correct Answer: C) $270^\circ$. 32. What is the sum of the squares of the direction ratio A) 1. B) 0. C) R$^{2}$. D) None of the above. Show Answer Correct Answer: C) R$^{2}$. 33. If A and B are two negative vectors, then ..... A) A =-B. B) A = B. C) A = 1/B. D) A =-1/B. Show Answer Correct Answer: A) A =-B. 34. Given two vectors A and B, where A is parallel to the y axis, and B is parallel to x axis. Find their dot product. A) $0$. B) 0 Mathematical EquivalenceON. C) All the above. D) None of the above. Show Answer Correct Answer: A) $0$. 35. If AB is denoted by a, then AB in opposite direction is denoted by A) A-. B) -a. C) A cap. D) None of the above. Show Answer Correct Answer: B) -a. 36. Gauss's Divergence Theorem relates A) Volume and Line Integrals. B) Surface and Line Integrals. C) Voulme and Surface Integrals. D) Any two integrals. Show Answer Correct Answer: C) Voulme and Surface Integrals. 37. Which on is true for a vector A) Directed line. B) Line segment. C) Directed line segment. D) None. Show Answer Correct Answer: C) Directed line segment. 38. What is the vector whose initial point is (-2, 4, 5) and terminal point is (1, 2, 3). A) 3i-2j-2k. B) 3i+2j+2k. C) -3i-2j-2k. D) -3i+2j+2k. Show Answer Correct Answer: A) 3i-2j-2k. 39. What is the vector called when it has the origin and a point as its initial and terminal points? A) Collinear Vector. B) Unit Vector. C) Position Vector. D) Zero Vector. Show Answer Correct Answer: C) Position Vector. 40. $\nabla\cdot B=?$ A) $-$. B) $\pm$. C) 0. D) $+$. Show Answer Correct Answer: C) 0. 41. Which of the following represent the vector going from the point (2, 3) to the origin? A) <-3, -2>. B) <2, 3>. C) <-2, -3>. D) (-2, -3). Show Answer Correct Answer: C) <-2, -3>. 42. The vector projection of u=(3, 2) onto vector v=(5, -5) is A) (1/2, 1/2). B) (1/2, -1/2). C) (-1/2, 1/2). D) (-1/2, -1/2). Show Answer Correct Answer: B) (1/2, -1/2). 43. Value of $\alpha$ $\alpha\overleftarrow{i}+\overleftarrow{j}+4\overleftarrow{k}$ $2\overleftarrow{i}+6j+3k$ A) 6. B) 12. C) 10. D) 5. Show Answer Correct Answer: D) 5. 44. If two vectors A and B have equal magnitude but opposite directions, then each vector is ..... vector of the other. A) Negative. B) Zero. C) UNIT. D) Positive. Show Answer Correct Answer: A) Negative. 45. Let a = <-2, 0> and b = <-4, -8>.Find a-b. A) <-6, 8>. B) <2, -8>. C) <2, 8>. D) <-6, -8>. Show Answer Correct Answer: C) <2, 8>. 46. Scalar (or Dot) product of two vectors always give a scalar quantity (or number) A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 47. If two vectors are collinear, what can be said about their direction? A) They have different magnitudes. B) They are parallel. C) They are always opposite. D) They are always equal. Show Answer Correct Answer: B) They are parallel. 48. Which of the following pair of vectors represents inverse vectors? A) A = (3, 4 ) and b = (-3, 4). B) A = (3, 4 ) and b = (-3, -4). C) A = (3, 4 ) and b = (3, 4). D) A = (3, 4 ) and b = (3, -4). Show Answer Correct Answer: B) A = (3, 4 ) and b = (-3, -4). 49. The magnitude of vector $\overrightarrow{A}=3\overrightarrow{a_x}+4\overrightarrow{a_y}+10\overrightarrow{a_z}$ A) $5\sqrt[]{5}$. B) $25$. C) 125. D) 225. Show Answer Correct Answer: A) $5\sqrt[]{5}$. 50. There are how many types of product for two vectors? A) 4. B) 1. C) 2. D) 3. Show Answer Correct Answer: C) 2. 51. What is the scalar product of two vectors a and b with an angle theta between them? A) |a||b|cot(theta). B) |a||b|tan(theta). C) |a||b|sin(theta). D) |a||b|cos(theta). Show Answer Correct Answer: D) |a||b|cos(theta). 52. Calculate the cross product of <1, -2, 1> and <2, -1, 1> A) 3. B) <-1, -1, 3>. C) 5. D) <-1, 1, 3>. Show Answer Correct Answer: D) <-1, 1, 3>. 53. Find the cross product of (3, 4, 7) and (4, 9, 2). A) (-55, 22, -9). B) (-55, -22, -9). C) (71, 34, 63). D) (-71, -34, -630. E) None of these. Show Answer Correct Answer: A) (-55, 22, -9). 54. If w = <2, -5> and y = <2, 0>, find 2w + y A) <6, -10>. B) <4, -5>. C) <-6, 10>. D) <-10, 2>. Show Answer Correct Answer: A) <6, -10>. 55. If A and B are matrices of same order then (AB'-BA$^{'}$) is A) Unit matrix. B) Skew symmetric matrix. C) Null matrix. D) Symmetric matrix. Show Answer Correct Answer: B) Skew symmetric matrix. 56. What is the sum of multiple vectors called? A) Rectangle. B) Tail. C) Head. D) Resultant vector. Show Answer Correct Answer: D) Resultant vector. 57. What is the term for the vector that represents the difference between two vectors? A) Negative Vector. B) Difference Vector. C) Resultant Vector. D) Displacement Vector. Show Answer Correct Answer: B) Difference Vector. 58. Which one is parallel vector of 3i+2j+5k A) -5k-2j-3i. B) -3i-2j+5k. C) 5k+2j-3i. D) 2i+3j-5k. Show Answer Correct Answer: A) -5k-2j-3i. 59. Given v = <-2, 5>, find-v A) <-5, 2>. B) <2, -5>. C) <-2, 5>. D) <5, -2>. Show Answer Correct Answer: B) <2, -5>. 60. If $\overrightarrow{a}\overrightarrow{, b, }\overrightarrow{c}$ $\overrightarrow{a}$ $\overrightarrow{b}$ $\overrightarrow{c}$ $\overrightarrow{a}\left(\overrightarrow{b}\times\overrightarrow{c}\right)$ A) $\overrightarrow{0}$. B) $\overrightarrow{a}$. C) $\overrightarrow{b}$. D) $\overrightarrow{c}$. Show Answer Correct Answer: A) $\overrightarrow{0}$. Next →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 10 Vector Algebra Quiz 2Class 12 Mathematics Chapter 10 Vector Algebra Quiz 3Class 12 Mathematics Chapter 10 Vector Algebra Quiz 4Class 12 Mathematics Chapter 1 Relations And Functions QuizClass 12 Mathematics Chapter 11 Three Dimensional Geometry QuizClass 12 Mathematics Chapter 12 Linear Programming QuizClass 12 Mathematics Chapter 13 Probability QuizClass 12 Mathematics Chapter 2 Inverse Trigonometric Functions Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books