Vector Algebra Test

Result

Vector Algebra Test - 12

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Question 1
4 / -1

If C is the mid - point of AB and P is any point outside AB, then

A
PA + PB = PC

B
PA + PB + 2PC = 0

C
PA + PB – 2PC = 0

D
PA + PB + PC = 0
Question 2
4 / -1

Let a, b and c be three non - zero vectors such that no two of these are collinear. If the vector a + 2b is collinear with C, then a + 2b + 6c is equals to

A
λ a (λ ≠ 0, a scalar )

B
λ b (λ ≠ 0, a scalar )

C
λ c (λ ≠ 0, a scalar )

D
0

Solution
Question 3
4 / -1

A
0

B
1

C
–2

D
2

Solution
Question 4
4 / -1

If a = (2, 1, –1), b = (1, –1, 0), c = (5, –1, 1), then unit vector parallel to a + b – c but in opposite direction is

A

B

C

D
None of these

Solution
Question 5
4 / -1

In a quadrilateral ABCD, the point P divides DC in the ration 1 : 2 and Q is the mid - point of AC. If AB + 2AD + BC – 2DC = kPQ, then k is equal to

A
–6

B
–4

C
6

D
4
Question 6
4 / -1

A
m₃ < m₁ < m₄ < m₂

B
m₃ < m₁ < m₂ < m₄

C
m₃ < m₄ < m₁ < m₂

D
m₃ < m₄ < m₂ < m₁
Question 7
4 / -1

A, B, C, D, E, and F in that order, are the vertices of a regular hexagon with centre origin. If the position vectors of the vertices A and B are respectively,

A

B

C

D

Solution
Question 8
4 / -1

A
1

B
4

C
3

D
no value of m for which vectors are coplanar

Solution
Question 9
4 / -1

A

B

C

D
Question 10
4 / -1

The non - zero vectors a, b and c are related by a = 8 b and c = – 7b. Then, the angle between a and c is

A
π

B
0

C
π/4

D
π/2

Solution