Question

If $a$ makes an acute angle with $b , r \cdot a =0$ and $r \times b = c \times b$, then $r =$

• A. $a \times c-b$
• B. $c \times a$
• C. $c-\left(\frac{ c \cdot a }{b \cdot a}\right) b$
• D. $c+\left(\frac{c \cdot a}{b \cdot a}\right) b$

Answer 1

The Correct Option is C

Given,
and $ r \cdot a =0 $
$ r \times b = c \times b $
So, $ a \times( r \times b )= a \times( c \times b ) $
$\Rightarrow r ( a \cdot b )- b ( a \cdot r )= c ( a \cdot b )- b ( a \cdot c ) $
$ \Rightarrow r ( a \cdot b )= c ( a \cdot b )- b ( a \cdot c ) $
$ \Rightarrow r = c - b \left(\frac{ c \cdot a }{ a \cdot b }\right)$