NCERT Solutions for class 12 Maths | Chapter 10 - Vector Algebra
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.
are 0, 5 and 8 respectively. Find the vector.
A
B
C
D
Answer:
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are
4
If a, b, c are unit vectors, then |a – b| + |b – c| + |c – a| does not exceed
Answer:9
and c =
are coplanar.
are coplanar, then the value
7
The volume of the parallelopiped whose edges are represented by 
and 
is 546 cu. units. Then α =
and is 546 cu. units. Then α =
Answer:-3
8
If the vectors 
form three concurrent edges of a parallelopiped, then the volume of the parallelopiped is
form three concurrent edges of a parallelopiped, then the volume of the parallelopiped is
Answer:4
9
The volume of the tetrahedron whose conterminous edges are 
is
is
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
Answer:u.v × w
11
If a, b, c are three non-coplanar vectors, then (a + b + c).[(a + b) × (a + c)] is
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
Answer:12√3
13
The vector 
is rotated through an angle θ and doubled in magnitude, then it becomes 
The value of x is
is rotated through an angle θ and doubled in magnitude, then it becomes The value of x is
Answer:{−2/3,2}
and 
are collinear, if
form the sides of
17
If (1/2,1/3,n) are the direction cosines of a line, then the value of n is
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
Answer:√593
then the value of a is
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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