Question

There are 6 vectors: a, b, c, d, e, f. Simply the following expression: [ a(b . c) X (e . f)d ] X [ a – d ].‘X’ represents cross product while ’.‘ represents dot product. Vectors a & d are perpendicular.

(a) 0

(b) (b . c)(e . f) [ d + a ]

(c) (b . c)(e . f) [ d – a ]

(d) (b . c)(e . f) [ d X a ]

This question was posed to me during a job interview.

This interesting question is from Vector Product of Two Vectors in division System of Particles and Rotational Motion of Physics – Class 11

Answer 1

Correct option is (b) (b . c)(e . f) [ d + a ]

Easiest explanation: [ a(b . c) X (e . f)d ] X [ a – d ]

= (b . c)(e . f) { [ a X d ] X [ a – d ] }

= (b . c)(e . f) { [ (a X d) X a ] – [ (a X d) X d ] }

Now, (a X d) is perpendicular to the plane of a & d. Refer to the diagram below.

We see that (a X d) X a = d    &    (a X d) X d = −a.

Therefore, our expression = (b . c)(e . f) [ d + a ].