If (a) makes an acute angle with (b , r \cdot a =0) and (r \... | Mathematics | SolveeIt

Question

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

$a \times c-b$

$c \times a$

$c-\left(\frac{ c \cdot a }{b \cdot a}\right) b$

$c+\left(\frac{c \cdot a}{b \cdot a}\right) b$

Answer

$c-\left(\frac{ c \cdot a }{b \cdot a}\right) b$

Explanation

Solution

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

Mathematics Question on Product of Two Vectors

Solution