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Multiplication with Vectors

A particle mo...

Question

A particle moves on a given line with a constant speed v. At a certain time it is at a point P on its straight line path. O is fixed point. Show that $(- - \to O P \times \to v)$ is independent of the position P.

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Solution

Let $\to v = v^i$
$- - \to O P = x^i + y^j$
Take $- - \to O P \times \to v = (x^i + y^j) \times v^i$ $= - y v^k$ ( $∴$ y is constant)
which is independent of position.

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