a, d are parallel and b, c are parallel

JEE Questions for Maths Vector Algebra Quiz 5

If a × b = 0 and a ∙ b = 0, then

0%
a ⊥ b
0%
a || b
0%
a = 0 and b = 0
0%
a = 0 or b = 0

If a = (1, p, 1), b = (q, 2, 2), a . b = r and a × b = (0, –3, 3), then p, q, and r are in that order

0%
1, 5, 9
0%
9, 5, 1
0%
5, 1, 9
0%
None of these

0%
0%
0
0%
0%

If [a × b b × c c × a] = λ[a b c]², then λ is equal to

0%
0
0%
1
0%
2
0%
3

If r = αb × c + βc × a + γa × b and [a b c] = 2, then α + β + γ is equal to

0%
r . [b × c + c × a + a × b]
0%
1/2 r . (a + b + c)
0%
2r . (a + b + c)
0%
4

The value of [(a – b) (b – c) (c – a)] is

0%
0
0%
1
0%
2 [a b c]
0%
2

0%
3
0%
10
0%
9
0%
6

If u, v and w are the three non - coplanar vectors, then (u + v – w) ∙ [(u – v) × (v – w)] is equal to

0%
u ∙ w × u
0%
u ∙ v × w
0%
0
0%
3 u ∙ v × w

0%
5
0%
20
0%
10
0%
30

0%
A = 4, B = 2, C = 3, D = 1
0%
A = 2, B = 3, C = 1, D = 4
0%
A = 3, B = 4, C = 1, D = 2
0%
A = 1, B = 4, C = 3, D = 2

If a, b and c are three non - coplanar vectors and p, q and r are vectors defined by
Maths-Vector Algebra-58924.png

0%
0
0%
1
0%
2
0%
3

If the volume of the parallelopiped formed by three non - coplanar vectors a, b and c is 4 cu units, then [a × b b × c c × a] is equal to

0%
64
0%
16
0%
4
0%
8

0%
–3
0%
5
0%
3
0%
–5

0%
– (1/2)
0%
– (1/3)
0%
– (1/6)
0%
1/6

For the non - zero vectors a, b and c the relation a. (b × c) = 0 is true, if

0%
b ⊥ c
0%
a ⊥ b
0%
a || c
0%
a ⊥ c

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a, b, c are non- coplanar
0%
a, b, d are non- coplanar
0%
b, d are non -parallel
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a, d are parallel and b, c are parallel

If u, v, w are non - coplanar vectors and p, q are real numbers, then the equality [3 u p v p w] – [p v w q u] – [2 w q v q u] = 0 holds for

0%
exactly two values of (p, q)
0%
more than two but not all values of (p, q)
0%
all values of (p, q)
0%
exactly one value of (p, q)

If a and b are two non - zero, non - collinear vectors, then
Maths-Vector Algebra-58929.png

0%
2 (a × b)
0%
a × b
0%
a + b
0%
None of these

The volume of the tetrahedron having the edges
Maths-Vector Algebra-58930.png

0%
1
0%
2
0%
3
0%
4

The edges of a parallelopiped are of unit length and are parallel to non - coplanar unit vectors
Maths-Vector Algebra-58931.png

0%
1/√2 cu unit
0%
1/2√2 cu unit
0%
√3/2 cu unit
0%
1/√3 cu unit

0%
α = 1, β = 1
0%
α = 2, β = 2
0%
α = 1, β = 2
0%
α = 2, β = 1

If the volume of a parallelopiped with a × b, b × c, c × a as conterminous edges is 9 cu units, then the volume of the parallelopied with (a × b) × (b × c) , (b × c) × (c × a) (c × a) × (a × b) as cotermimous edges is

0%
9 cu units
0%
729 cu units
0%
81 cu units
0%
27 cu units
0%
243 cu units

0%
A = 3, B = 1, C = 2, D = 6
0%
A = 3, B = 1, C = 6, D = 5
0%
A = 1, B = 3, C = 2, D = 6
0%
A = 1, B = 3, C = 6, D = 4

0%
4
0%
–13
0%
13
0%
6

0%
zero
0%
one
0%
two
0%
three

If a is perpendicular to b and c , |a|= 2, |b| = 3, |c| = 4 and the angle between b and c is 2π/3 , then [a b c] is equal to

0%
4√3
0%
6√3
0%
12√3
0%
18√3

a . [(b + c) × (a + b + c)] is equal to

0%
0
0%
a + b + c
0%
a
0%
a. (b + c)

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

0%
π/3
0%
π/4
0%
π/6
0%
π/2
0%
π/12

The value of [a b + c a + b + c] is

0%
[a b c]
0%
0
0%
2 [a b c]
0%
a × (b × c)

If a, b, c are non - coplanar and [a + b b + c c + a] = k [a b c], then k is equal to

0%
0
0%
1
0%
2
0%
3

0%
1
0%
0
0%
–√3
0%
√3
0%
6

0%
π/6
0%
π/4
0%
π/2
0%
π/3

0%
0%
2)
0%
0%

If a is perpendicular to b, then the vector a × {a × (a × b)} is equal to

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

0%
0%
2)
0%
0%

0%
3/2
0%
2/3
0%
2
0%
√3/2

If a, b and c be three unit vectors such that a × (b × c) = 1/2 b, b and c being non - parallel. If θ₁ is the angle between a and b and θ₂ is the angle between a and c, then

0%
0%
2)
0%
0%

Let a, b and c be non - zero vectors such that (a × b) × c = –1/4|b| |c| a. If θ is the acute angle between the vectors b and c, then the angle between a and c is

0%
2π/3
0%
π/4
0%
π/3
0%
π/2

The vector a × (b × c) is coplanar with the vectors

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

If b is unit vector, then (a ∙ b) b + b × (a × b) is

0%
|a|2 b
0%
|a ∙ b|a
0%
a
0%
b

0%
0%
2)
0%
0%

0%
0%
2)
0%
0%

If a × (b × c) = (a × b) × c, where a, b and c are any three vectors such that a ∙b ≠ 0 , c ≠ 0, then a and c are

0%
inclined at an angle of π/6 between then
0%
perpendicular
0%
parallel
0%
inclined at angle of π/3, between them

If a and b are unit vectors, then the vector (a + b) × (a × b) is parallel to the vector

0%
a – b
0%
a + b
0%
2a – b
0%
2a + b

0%
0%
2)
0%
0%

A, B and C are three non - zero vectors, no two of them are parallel. If A + B is collinear to C and B + C is collinear to A, then A + B + C is equal to