If x.a=0,x×b=c×b then x =

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Question

If

x . a = 0, x \times b = c \times b

then x =

Options:

A . c−c.ab.ab

B . c−c.ab.aa

C . a−c.ab.ab

D . b−c.ab.ab

Answer: Option A
:
A

x \times b = c \times b \Rightarrow (x - c) \times b = 0 \Rightarrow x - c

is parallel to b

\Rightarrow x - c = λ b

for some scalar

λ \Rightarrow x = c + λ b

x . a = 0 \Rightarrow (c + λ b) . a = 0 \Rightarrow c . a + λ b . a = 0 \Rightarrow λ = - \frac{c . a}{b . a} \Rightarrow x = c - \frac{c . a}{b . a} b

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