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

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Questions
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 class 12 maths chapter 10 vector algebra 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 = class 12 maths chapter 10 vector algebra and c = are coplanar.
A 4
B -2
C -6
D 5

Answer:4
6 If the vectors class 12 maths chapter 10 vector algebra 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 class 12 maths chapter 10 vector algebra 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 class 12 maths chapter 10 vector algebra 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 class 12 maths chapter 10 vector algebra 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 class 12 maths chapter 10 vector algebra
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 class 12 maths chapter 10 vector algebra 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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