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  • True and False If |a +b| equals |a -b| , then the vectors a and b are orthogonal.

True and False

If |\vec{a}+\vec{b}|=|\vec{a}-\vec{b}| , then the vectors \vec{a}  and \vec{b}  are orthogonal.

Answers (1)

True

Explanation:

Given that, |\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|

On squaring both the sides, we get

\\ \Rightarrow|\vec{a}+\vec{b}|^{2}=|\vec{a}-\vec{b}|^{2} \\ \Rightarrow \vec{a}^{2}+2 \vec{a} \cdot \vec{b}+\vec{b}^{2}=\vec{a}^{2}-2 \vec{a} \cdot \vec{b}+\vec{b}^{2} \\ \Rightarrow 2 \vec{a} \cdot \vec{b}=-2 \vec{a} \cdot \vec{b} \\ \Rightarrow 2 \vec{a} \cdot \vec{b}+2 \vec{a} \cdot \vec{b}=0 \\ \Rightarrow 4 \vec{a} \cdot \vec{b}=0\\ \Rightarrow \vec{a} \cdot \vec{b}=0

Hence,  \vec{a}  and \vec{b}  are orthogonal.

Posted by

infoexpert22

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