# If → a × → B = → B × → C ≠ 0 , Then Show that → a + → C = M → B , Where M is Any Scalar. - Mathematics

Sum

if $\vec{a} \times \vec{b} = \vec{b} \times \vec{c} \neq 0,$  then  show that $\vec{a} + \vec{c} = m \vec{b} ,$  where m is any scalar.

#### Solution

$\vec{a} \times \vec{b} = \vec{b} \times \vec{c}$
$\Rightarrow \vec{a} \times \vec{b} = - \vec{c} \times \vec{b}$
$\Rightarrow \vec{a} \times \vec{b} + \vec{c} \times \vec{b} = 0$
$\Rightarrow \left( \vec{a} + \vec{c} \right) \times \vec{b} = 0 (\text{ Using right distributive property } )$
$\text{ Thus } , \vec{a} + \vec{c} \text{ is parallel to } \vec{b} .$
$\Leftrightarrow \vec{a} + \vec{c} = m \vec{b} , \text{ for some scalarm } .$

Is there an error in this question or solution?

#### APPEARS IN

RD Sharma Class 12 Maths
Chapter 25 Vector or Cross Product
Exercise 25.1 | Q 15 | Page 30