NDA 2019 Maths · Mathematics · Vector Algebra · hard

If [vec a vec b vec c]=vec a·(vec b×vec c)=4, then (vec a+vec b)·[(vec b+vec c)×(vec c+vec a)] equals

Single correct option

[\vec a\;\vec b\;\vec c]=\vec a\cdot(\vec b\times\vec c)=4

, then

(\vec a+\vec b)\cdot\big[(\vec b+\vec c)\times(\vec c+\vec a)\big]

equals

Show answer and solution

Answer: (B) $8$

Expand:

(\vec b+\vec c)\times(\vec c+\vec a)=\vec b\times\vec c+\vec b\times\vec a+\vec c\times\vec a

(since

\vec c\times\vec c=\vec0

). Dotting with

\vec a+\vec b

, only terms with three distinct vectors survive:

\vec a\cdot(\vec b\times\vec c)+\vec b\cdot(\vec c\times\vec a)=4+4=8

. In general the value is

2[\vec a\;\vec b\;\vec c]

Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake