If x . a = 0 , x × b = c × b then x = Options: A . &nbsp c − c . a b . a b B . &nbsp c − c . a b . a a C . &nbsp a − c . a b . a b D . &nbsp b − c . a b . a b

Answer: Option A : A x × b = c × b ⇒ ( x − c ) × b = 0 ⇒ x − c is parallel to b ⇒ x − c = λ b for some scalar λ ⇒ x = c + λ b x . a = 0 ⇒ ( c + λ b ) . a = 0 ⇒ c . a + λ b . a = 0 ⇒ λ = − c . a b . a ⇒ x = c − c . a b . a b

If x.a=0,x×b=c×b then x =

Discussion Forum : Vector Algebra

Question -

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

Options:

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: 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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