Question

If $a$ and $b$ are two unit vectors, then the vector $(a+b)\times (a\times b)$ is parallel to the vector

• A. $a-b$
• B. $a+b$
• C. $2a-b$
• D. $2a+b$

Answer 1

Answer: (A)

$a-b$

We have, $(a+b)\times (a\times b)$

$=a\times (a\times b)+b\times (a\times b)$

$=(a.b)a-(a.a)b+(b.b)a-(b.a)b$

$=(a.b)(a-b)+a-b(b.b=b^2=1,a.a=a^2=1$ as $a.b$ are unit vectors)

$=(a.b+1)(a-b)$

$=x(a-b),$, where $x=a.b+1$ is a scalar.

$\therefore$ The given vector is parallel to $a-b.$