Question

if if A and B are two vectors then the value of a vector + b vector cross a vector minus b vector is ​

Answer 1

$\textbf{Concept used:}$

$\text{For any non-zero vector \overrightarrow{a} , \overrightarrow{a}{\times}\overrightarrow{a}=\overrightarrow{0} }$

$\textbf{Given:}$

$\text{ \overrightarrow{a} and \overrightarrow{b} be any two vectors}$

$\textbf{To find:}$

$(\overrightarrow{a}+\overrightarrow{b}){\times}(\overrightarrow{a}-\overrightarrow{b})$

$=(\overrightarrow{a}{\times}\overrightarrow{a})-(\overrightarrow{a}{\times}\overrightarrow{b})+(\overrightarrow{b}{\times}\overrightarrow{a})-(\overrightarrow{b}{\times}\overrightarrow{b})$

$=\overrightarrow{0}-(\overrightarrow{a}{\times}\overrightarrow{b})+(\overrightarrow{b}{\times}\overrightarrow{a})-\overrightarrow{0}$

$\text{We know that,}$

$\boxed{\bf\;\overrightarrow{a}{\times}\overrightarrow{b}=-(\overrightarrow{b}{\times}\overrightarrow{a})}$

$=-(\overrightarrow{a}{\times}\overrightarrow{b})-(\overrightarrow{a}{\times}\overrightarrow{b})$

$=-2(\overrightarrow{a}{\times}\overrightarrow{b})$

$\therefore\boxed{\bf(\overrightarrow{a}+\overrightarrow{b}){\times}(\overrightarrow{a}-\overrightarrow{b})=-2(\overrightarrow{a}{\times}\overrightarrow{b})}$

Find more:

If |a| = 13,|b|= 5 and a.b = 60, then

find la xbl.

https://brainly.in/question/12537337

Answer 2

Step-by-step explanation:

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