If a makes an acute angle with b , r ⋅ a =0 and r × b = c × b, then r =

Question

If a makes an acute angle with b , r ⋅ a =0 and r × b = c × b, then r = (A) a × c-b (B) c × a (C) c-(( c ⋅ a /b ⋅ a)) b (D) c+((c ⋅ a/b ⋅ a)) b

Tardigrade Admin · Accepted Answer

Given, and r ⋅ a =0 r × b = c × b So, a ×( r × b )= a ×( c × b ) ⇒ r ( a ⋅ b )- b ( a ⋅ r )= c ( a ⋅ b )- b ( a ⋅ c ) ⇒ r ( a ⋅ b )= c ( a ⋅ b )- b ( a ⋅ c ) ⇒ r = c - b (( c ⋅ a / a ⋅ b ))

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

$a \times c - b$

$c \times a$

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

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

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

Q. If a makes an acute angle with b,r⋅a=0 and r×b=c×b, then r=

a×c−b

c×a

c−(b⋅ac⋅a​)b

c+(b⋅ac⋅a​)b