If $|\overrightarrow{\mathbf{a}}\mathbf{| = |}\overrightarrow{\mathbf{b}}|$, then $(\overrightarrow{\mathbf{a}}\mathbf{+}\overrightarrow{\mathbf{b}}) \bullet (\overrightarrow{\mathbf{a}}\mathbf{-}\overrightarrow{\mathbf{b}})$ is

Question

Dr. Abubacker · Accepted Answer

(c)
Given that, $|\overrightarrow{\mathbf{a}}| = |\overrightarrow{\mathbf{b}}|$
Now, $\left( \overrightarrow{\mathbf{a}} + \overrightarrow{\mathbf{b}} \right) \bullet \left( \overrightarrow{\mathbf{a}} - \overrightarrow{\mathbf{b}} \right) = \overrightarrow{\mathbf{a}}\mathbf{\bullet}\overrightarrow{\mathbf{a}}\mathbf{+}\overrightarrow{\mathbf{b}}\mathbf{\bullet}\overrightarrow{\mathbf{a}}\mathbf{-}\overrightarrow{\mathbf{b}}\mathbf{\ }\overrightarrow{\mathbf{a}}\mathbf{-}\overrightarrow{\mathbf{b}}\mathbf{\ }\overrightarrow{\mathbf{b}}$
$= 0\ \ (\because\ \mathbf{|}\overrightarrow{\mathbf{a}\mathbf{|}}\mathbf{= |}\overrightarrow{\mathbf{b}\mathbf{|}})$

Q. If $|\overrightarrow{\mathbf{a}}\mathbf{| = |}\overrightarrow{\mathbf{b}}|$, then $(\overrightarrow{\mathbf{a}}\mathbf{+}\overrightarrow{\mathbf{b}}) \bullet (\overrightarrow{\mathbf{a}}\mathbf{-}\overrightarrow{\mathbf{b}})$ is

Explanation

Reviewed by Dr. Abubacker

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