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NCERT Solutions for class 12 Maths | Chapter 10 - Vector Algebra

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Free download in PDF Class 12 Maths Chapter 10 Vector Algebra Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 12 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>

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(1) If a, b, c are three mutually perpendicular vectors of equal magnitude, find the angle between a and a + b + c.
[A]
[B]
[C]
[D]
Answer:
(2) The dot product of a vector with the vectors are 0, 5 and 8 respectively. Find the vector.
[A]
[B]
[C]
[D]
Answer:

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(3) Find the value of λ so that the vectors are
[A] -15
[B] 10
[C] -40
[D] 20
Answer: -40
(4) If a, b, c are unit vectors, then |a – b| + |b – c| + |c – a| does not exceed
[A] 4
[B] 9
[C] 8
[D] 6
Answer: 9
(5) Find the value of λ if the vectors, a = and c = are coplanar.
[A] 4
[B] -2
[C] -6
[D] 5
Answer: 4
(6) If the vectors are coplanar, then the value
[A] 0
[B] 1
[C] 2
[D] 3
Answer: 0
(7) The volume of the parallelopiped whose edges are represented by and is 546 cu. units. Then α =
[A] 3
[B] 2
[C] -3
[D] -2
Answer: -3
(8) If the vectors form three concurrent edges of a parallelopiped, then the volume of the parallelopiped is
[A] 8
[B] 10
[C] 4
[D] 14
Answer: 4
(9) The volume of the tetrahedron whose conterminous edges are is
[A] 1/6 cu. unit
[B] 1/3 cu. unit
[C] 1/2 cu. unit
[D] 2/3 cu. unit
Answer: 1/3 cu. unit
(10) If u, v and w are three non-coplanar vectors, then (u + v – w).[(u – v) × (v – w)] equals
[A] 0
[B] u.v × w
[C] u.w × v
[D] 3u.v × w
Answer: u.v × w
(11) If a, b, c are three non-coplanar vectors, then (a + b + c).[(a + b) × (a + c)] is
[A] 0
[B] 2[abc]
[C] -[abc]
[D] [abc]
Answer: -[abc]
(12) If a is perpendicular to b and c, |a| = 2, |b| = 3, |c| = 4 and the angle between b and c is 2π/3, |abc| is equal to
[A] 4√3
[B] 6√3
[C] 12√3
[D] 18√3
Answer: 12√3
(13) The vector is rotated through an angle θ and doubled in magnitude, then it becomes The value of x is
[A] {−2/3,2}
[B] {1/3,2}
[C] {2/3,0}
[D] {2, 7}
Answer: {−2/3,2}
(14) The vectors and are collinear, if
[A] x =1, y = -2, z = -5
[B] x= 1.2, y = -4, z = -10
[C] x = -1/2, y = 4, z = 10
[D] All of these
Answer: All of these
(15) The vectors form the sides of
[A] Isosceles triangle
[B] Right triangle
[C] Scalene triangle
[D] Equilaterala triangle
Answer: Equilaterala triangle
(16) Find the magnitude of vector
[A] √157
[B] 4√11
[C] √213
[D] 9√3
Answer: √157
(17) If (1/2,1/3,n) are the direction cosines of a line, then the value of n is
[A] √23/6
[B] 23/6
[C] 2/3
[D] 3/2
Answer: √23/6
(18) The length of longer diagronai of the parallelogram constructed on 5a + 2b and a – 3b. If it is given that |a| = 2√2, |b| = 3 and angle between a and b is π4, is
[A] 15
[B] √113
[C] √593
[D] √369
Answer: √593
(19) If the angle between then the value of a is
[A] 0 or 2
[B] -4 or 0
[C] 0 or -3
[D] 2 or -2
Answer: -4 or 0
(20) If a and b are two unit vectors inclined to x-axis at angles 30° and 120° respectively, then |a + b| equals
[A]
[B] √2
[C] √3
[D] 2
Answer: 2

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