Question

Which of the following is correct :
(a) A➝ . B➝ ≠ B➝ . A➝
(b) A➝ . (B➝ + C➝) = A . B + A➝ .C➝
(c) A➝x B➝ = B➝ x A
(d) A➝ . (B➝ + C➝ ) ≠ A➝ . B➝ + A➝ .C➝

Answer 1

Vector dot (.) product :

If A and B be two vectors, then their dot product is defined by

A . B = A B cosθ,

where θ is the angle between A and B.

Vector cross (×) product :

If A and B be two vectors, then their cross product is defined by

A × B = A B sinθ,

where θ is the angle between A and B.

Now we proceed to find the required answer.

Option (A)

A . B ≠ B . A

This is incorrect because dot product is commutative, i.e., a . b = b . a

Option (B)

A . (B + C) = A . B + A . C

This is correct because dot product is distributive, i.e., a . (b + c) = a . b + a . c

Option (C)

A × B = B × A

This is incorrect because cross product is not commutative, i.e., a × b ≠ b × a

Option (D)

A . (B + C) ≠ A . B + A . C

This is incorrect because dot product is distributive, i.e., a . (b + c) = a . b + a . c

The correct option is Option (B).