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Vector Algebra

Question
CBSEENMA12034075
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straight a with rightwards arrow on top space and space straight b with rightwards arrow on top are two vectors such that open vertical bar straight a with rightwards arrow on top close vertical bar space equals 2 comma space space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 3 space and space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 3 comma find the angle between straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.

Solution

We have open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 2 comma space space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 3 comma space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 3
Let straight theta be the angle between straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.
therefore space space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals 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 straight theta space space space space space rightwards double arrow space space space 3 space equals space left parenthesis 2 right parenthesis thin space left parenthesis 3 right parenthesis space cos space straight theta therefore space space space space cos space straight theta space equals space 1 half space space space space space rightwards double arrow space space space space straight theta space equals space 60 degree

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