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Vector Algebra

Question
CBSEENMA12034078
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Find the magnitude of two vectors straight a with rightwards arrow on top space and space straight b with rightwards arrow on top having the same magnitude and such that the angle between them is 30° and their scalar product is 3.

Solution

Let straight theta be angle between straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.
therefore space space space straight theta space equals space 30 degree comma space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space open vertical bar straight b with rightwards arrow on top close vertical bar comma space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 3                              ...(1)
Now,              straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 3 space space space space rightwards double arrow space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space open vertical bar straight b with rightwards arrow on top close vertical bar space cos space 30 degree space equals space 3
rightwards double arrow space space space open vertical bar straight a with rightwards arrow on top close vertical bar space open vertical bar straight a with rightwards arrow on top close vertical bar space cross times fraction numerator square root of 3 over denominator 2 end fraction space equals space 3 space space space space space rightwards double arrow space space space open vertical bar straight a with rightwards arrow on top close vertical bar squared space equals space 2 square root of 3 space equals space 3.46 space space space space space space left square bracket because space of space left parenthesis 1 right parenthesis right square bracket therefore space space space space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 1.86 space equals space open vertical bar straight b with rightwards arrow on top close vertical bar

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