Vector Algebra Test

Result

Vector Algebra Test - 27

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Weekly Quiz Competition

Question 1
4 / -1

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

A
64

B
16

C
4

D
8
Question 2
4 / -1

A
–3

B
5

C
3

D
–5
Question 3
4 / -1

A
– (1/2)

B
– (1/3)

C
– (1/6)

D
1/6
Question 4
4 / -1

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

A
b ⊥ c

B
a ⊥ b

C
a || c

D
a ⊥ c
Question 5
4 / -1

A
a, b, c are non- coplanar

B
a, b, d are non- coplanar

C
b, d are non -parallel

D
a, d are parallel and b, c are parallel
Question 6
4 / -1

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

A
exactly two values of (p, q)

B
more than two but not all values of (p, q)

C
all values of (p, q)

D
exactly one value of (p, q)
Question 7
4 / -1

If a and b are two non - zero, non - collinear vectors, then

A
2 (a × b)

B
a × b

C
a + b

D
None of these
Question 8
4 / -1

The volume of the tetrahedron having the edges

A
1

B
2

C
3

D
4
Question 9
4 / -1

The edges of a parallelopiped are of unit length and are parallel to non - coplanar unit vectors

A
1/√2 cu unit

B
1/2√2 cu unit

C
√3/2 cu unit

D
1/√3 cu unit
Question 10
4 / -1

A
α = 1, β = 1

B
α = 2, β = 2

C
α = 1, β = 2

D
α = 2, β = 1