For any two vectors a - and b - write when a -b -a -b - holds-

Given #160;thata #8594;+b #8594;=a #8594; b #8594;Squaring #160;both #160;sides, #160;we #160;geta #8594;+b #8594;2=a #8594; b #8594;2 ...

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Vector Addition

For any two v...

Question

For any two vectors $\vec{a} and \vec{b}$ , write when $|\vec{a} + \vec{b}| = |\vec{a} - \vec{b}|$ holds.

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[\vec{a} \vec{b} \vec{a} \times \vec{b}] + (\vec{a} . \vec{b})

\vec{a} and \vec{b}

[\vec{a} \vec{b} \vec{a} \times \vec{b}] + {(\vec{a} \cdot \vec{b})}^{2} .

\vec{a} and \vec{b}

{|\vec{a} \times \vec{b}|}^{2} = |\begin{matrix} \vec{a} . \vec{a} & \vec{a} . \vec{b} \\ \vec{b} . \vec{a} & \vec{b} . \vec{b} \end{matrix}|

\vec{a} and \vec{b}

{(\vec{a} . \vec{b})}^{2} + {|\vec{a} \times \vec{b}|}^{2}

\frac{{|\vec{a} + \vec{b}|}^{2} + {|\vec{a} - \vec{b}|}^{2}}{{|\vec{a}|}^{2} + {|\vec{b}|}^{2}} .

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