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Physics Part I

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If straight A with rightwards arrow on top cross times straight B with rightwards arrow on top space equals space straight C with rightwards arrow on top cross times straight B with rightwards arrow on top, the do you think that A is necessarily equal to C?



Here,   straight A with rightwards arrow on top cross times straight B with rightwards arrow on top space equals space straight C with rightwards arrow on top cross times straight B with rightwards arrow on top
Let the angle between straight A with rightwards arrow on top space and space straight B with rightwards arrow on top be straight alpha and that between straight B with rightwards arrow on top and space straight C with rightwards arrow on top be straight beta.

∴            AB space sinα space stack straight n subscript 1 with hat on top space equals space CB space sin space straight beta space stack straight n subscript 2 with hat on top


rightwards double arrow           space AB space sinα space equals space CB space sinβ

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Therefore,
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rightwards double arrow                     straight A equals straight C sinβ over sinα


Now,   space space if space straight alpha space equals space straight beta comma space space then space straight A space equals space straight C

and       if space straight alpha not equal to straight beta comma    then straight A not equal to straight C


Thus, A is not necessarily equal to C.

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