Question

Which of the following is not correct :
(a) A➝x B➝ = -B➝x A
(b) A➝ x B➝ ≠ B ➝x A
(c) A➝ (B➝ + C➝) = A➝´xB➝ + A➝ xC➝
(d) A➝x (B➝ + C➝ ) = ( A➝x B➝) + C➝

Answer 1

Answer:

C) is the correct option.

Explanation:

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

Answer 2

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 correct because cross product is not commutative, but a × b = - b × a

Option (B)

A × B ≠ B × A

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

Option (C)

A × (B + C) = A × B + A × C

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

Option (D)

A × (B + C) = (A × B) + C

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

The incorrect option is Option (D).