Question

If $a$ is a unit vector, $a\times r=b,a.r=c,a.b=0$, then $r$ is

• A. $cb+(a\times b)$
• B. $ca+(a\times b)$
• C. $cb-(a\times b)$
• D. $ca-(a\times b)$

Answer 1

Answer: (D)

$ca-(a\times b)$

Given $a\times r=b,a.r=c$ and $a.b=0$

Since $a\times r=b$

$\therefore a\times (a\times r)=a\times b\Rightarrow (a.r)a-(a.a)r=a\times b\Rightarrow ca-a^{2}r=a\times b$

$\Rightarrow ca-r=a\times b$ $[\because a$ is unit vector $\therefore a^2=1]$

$\therefore r=ca-(a\times b)$