Question

If $x.a=0,x\times b=c\times b$ then x =

• A. $c-\frac{c.a}{b.a}b$
• B. $c-\frac{c.a}{b.a}a$
• C. $a-\frac{c.a}{b.a}b$
• D. $b-\frac{c.a}{b.a}b$

Answer 1

The correct option is A $c-\frac{c.a}{b.a}b$

$x\times b=c\times b\Rightarrow (x-c)\times b=0\Rightarrow x-c$ is parallel to b
$\Rightarrow x-c=\lambda b$ for some scalar $\lambda \Rightarrow x=c+\lambda b$
$x.a=0\Rightarrow (c+\lambda b).a=0\Rightarrow c.a+\lambda b.a=0\Rightarrow \lambda =-\frac{c.a}{b.a}\Rightarrow x=c-\frac{c.a}{b.a}b$