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Vector Algebra

Question
CBSEENMA12034072
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If 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 space 4 comma space space open vertical bar straight b with rightwards arrow on top close vertical bar space equals space 3 space space and space straight a with rightwards arrow on top comma space straight b with rightwards arrow on top space equals space 6 find the angle between straight a with rightwards arrow on top space and space straight b with rightwards arrow on top.

Solution

Here open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 4 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 6
Let straight theta be angle between straight a with rightwards arrow on top space and space straight b with rightwards arrow on top space equals space 6.
Now, 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 space space space space space space rightwards double arrow space space space space 6 space equals space left parenthesis 4 right parenthesis thin space left parenthesis 3 right parenthesis space cos space straight theta
rightwards double arrow space space space space cos space straight theta space equals space 1 half space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space rightwards double arrow space space space space straight theta space equals space 60 degree

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