If the dot product of two non-zero vectors is zero- then the vectorscan have any orientation-are anti-parallel to each other-are parallel to each other-are perpendicular to each other-

The correct option is D are perpendicular to each other.The scalar product will be zero when cosθ will be zero. ⇒ θ=90^∘, hence, the vectors will be perpendicu ...

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Standard XII

Physics

Infinite Sheet

If the dot pr...

Question

If the dot product of two non-zero vectors is zero, then the vectors

are parallel to each other.

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are perpendicular to each other.

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can have any orientation.

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are anti-parallel to each other.

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Solution

The correct option is D are perpendicular to each other.
The scalar product of two vectors $\to A$ and $\to B$ is given by.
$\to A . \to B = A B c o s θ$
where $θ$ is the angle between $\to A$ and $\to B$
The scalar product will be zero when $cos θ$ will be zero.
$\Rightarrow θ = 90^{\circ}$ , hence, the vectors will be perpendicular to each other.

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