a × b , b × c , c × a mutually perpendicular

Both A and R are correct and R is the correct reason for A

Both A and R are correct but R is not the correct reason for A

A is correct but R is incorrect

A is incorrect but R is correct

JEE Questions for Maths Vector Algebra Quiz 4

0%
0%
2)
0%
0%
None of these

If |a| = |b| = 1 and |a + b| = √3, then the value of (3a – 4b) . (2a + 5b) is

0%
–21
0%
– (21/2)
0%
21
0%
21/2

If a, b and c are three unit vectors such that a + b + c = 0 where 0 is null vector, then a∙b + b∙c + c∙a is equal to

0%
-3
0%
-2
0%
-3/2
0%
0

A force of magnitude √6 acting along the line joining the points A(2, –1,and B(3, 1,displaces a particle from A to B. The work done by the force is

0%
6
0%
6√6
0%
√6
0%
12
0%
2√6

0%
0%
2)
0%
0%

If |a| = 3, b = |4|, |c| = 5 and a, b, c are such that each is perpendicular to the sum of other two, then |a + b + c| is equal to

0%
5√2
0%
5/√2
0%
10√2
0%
10√3
0%
5√3

0%
60o
0%
90o
0%
45o
0%
55o

0%
√5
0%
√3
0%
0
0%
1

0%
–3/2
0%
6
0%
–6
0%
3

0%
0%
2)
0%
0%

If |a|= 1, |b| = 4, a.b = 2 and c = 2a × b – 3b, then the angle between b and c is

0%
π/6
0%
5π/6
0%
π/3
0%
2π/3

The area of the parallelogram whose adjacent side are
Maths-Vector Algebra-58861.png

0%
3
0%
√2
0%
4
0%
√3

0%
a × b = b × c = c × a = 0
0%
a × b = b × c = c × a ≠ 0
0%
a × b = b × c = a × c = 0
0%
a × b , b × c , c × a mutually perpendicular

0%
3
0%
6
0%
9
0%
12

|a| = |b| = 5 and the angle between a and b is π/4. The area of the triangle constructed on the vectors a – 2b and 3a + 2b is

0%
50
0%
50√2
0%
50/√2
0%
100

In a triangle with vertices A (1, –1, 2), B(5, –6,and C(1, 3, –1), find the altitude n = |BD|.

0%
5
0%
10
0%
5√2
0%
10/√2

0%
|a|2
0%
2|a|2
0%
3|a|2
0%
4|a|2

If a, b and c are three vectors such that a × b = c and b × c = a, then

0%
a ≠ b ≠ c
0%
a = b = c
0%
a ≠ b ≠ c ≠ 1
0%
a, b and c are orthogonal in pairs

0%
2/3
0%
3/2
0%
2
0%
3

If r∙a = r∙b = r∙c = 1. Where a , b and c are any three non - coplanar vectors, then r is

0%
coplanar with a, b and c
0%
parallel to a + b + c
0%
parallel to b × c + c × a + a × b
0%
parallel to (a × b) × c

If a and b are vectors such that |a + b| = √29 and
Maths-Vector Algebra-58869.png

0%
0
0%
3
0%
4
0%
8

If |a × b|² + |a ∙ b|² = 144 and |a| = 4, then |b| is equal to

0%
16
0%
8
0%
3
0%
12

The vectors a and b are not perpendicular and c and d are two vectors satisfying b × c = b × d and a ∙ d = 0. Then, the vector d is equal to

0%
0%
2)
0%
0%

If a and b represents the adjacent sides of a parallelogram whose area is 15 units, then the area of the parallelogram whose adjacent sides are 3a + 2b and a + 3b is

0%
45 units
0%
75 units
0%
105 units
0%
165 units

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%
0%

If |a|= 5, |b| = 6 and a. b = –25, then |a × b| is equal to

0%
25
0%
6√11
0%
11√5
0%
11√6
0%
5√11

Vectors a and b are inclined at an angle θ = 120^o . If |a| = 1, |b| = 2, then [(a + 3b) × (3a + b)]² is equal to

0%
190
0%
275
0%
300
0%
320
0%
192

If the projection of the vector a on b is |a × b| and if
Maths-Vector Algebra-58887.png

0%
π/3
0%
π/2
0%
π/4
0%
π/6
0%
0

(a – b) × (a + b) = ..., where a, b ϵ R³

0%
2(a × b)
0%
|a|2 – |b|2
0%
1/2 (a × b)
0%
None of these

0%
7
0%
–7
0%
–5
0%
5

If 2a + 3b + c = 0, then a × b + b × c + c × a is equal to

0%
6 (b × c)
0%
3 (b × c)
0%
2 (b × c)
0%
0

If b and c are any two non - collinear unit vectors and a is any vector, then
Maths-Vector Algebra-58889.png

0%
0
0%
a
0%
b
0%
c

0%
√21
0%
√21/2
0%
2√21
0%
√21/4

If |a|= 2, |b|=3 and a, b are mutually perpendicular, then the area of the triangle whose vertices are 0, a + b, a – b is

0%
5
0%
1
0%
6
0%
8

0%
0%
2)
0%
0%

If a, b and c are position vectors of the vertices of the ∆ABC, then
Maths-Vector Algebra-58897.png

0%
cot A
0%
cot C
0%
– tan C
0%
tan C
0%
tan A

If a × b = c × d and a × c = b × d, then

0%
(a – d) = λ ( b – c)
0%
(a + d) = λ ( b + c)
0%
(a – b) = λ ( c + d)
0%
(a + b) = λ (c – d)
0%
None of these

0%
a . b
0%
1
0%
0
0%
1/2

If a and b are any two vectors, then (2a + 3b) × (5a + 7b) + a × b is equal to

0%
0
0%
1
0%
a × b
0%
b × a

If the vectors PQ, QR, ST, TU and UP represents the sides of a regular hexagon. Then,
Statement I . PQ × (RS + ST) ≠ 0 because
Statement II . PQ × RS = 0 and PQ × ST ≠ 0

0%
Statement I is correct, Statement II is correct; Statement II is correct explanation for Statement I
0%
Statement I is correct, Statement II is correct; Statement II is not correct explanation for Statement I
0%
Statement I is correct; Statement II is incorrect
0%
Statement I is incorrect; Statement II is correct