If a a = 0 and a b = 0, then what can be concluded about the vect… - Vidyadip

Question

If $\vec { a } \cdot \vec { a } = 0$ and $\vec { a } \cdot \vec { b } = 0,$ then what can be concluded about the vector $\vec { b }$?

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Answer

Here ,we are given that $\vec { a } \cdot \vec { a } = 0 \Rightarrow | \vec { a } | ^ { 2 } = 0$
$\Rightarrow \quad | \vec { a } | = 0$ ......(1)
and $\vec { a } \cdot \vec { b } = 0$ ........(2)
$\Rightarrow \quad | \vec { a } | | \vec { b } | \cos \theta = 0$
From Eqs. (1) and (2), it may be concluded that $\vec { b }$ is either zero or non-zero perpendicular vector.

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