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Vector Algebra

Question
CBSEENMA12034079
Wired Faculty App

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 then is 60° and their scalar product is 1/2.

Solution

Here open vertical bar straight a with rightwards arrow on top close vertical bar space equals open vertical bar straight b with rightwards arrow on top close vertical bar comma space space space straight theta space equals space 60 degree comma space space straight a with rightwards arrow on top. space straight b with rightwards arrow on top space equals space 1 half                        ...(1)
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 rightwards double arrow space space space space 1 half space equals 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 cos space 60 degree space space space space space space space space space space open square brackets because space of space left parenthesis 1 right parenthesis close square brackets
rightwards double arrow space space 1 half space equals open vertical bar straight a with rightwards arrow on top close vertical bar squared space cross times space 1 half space space space 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 1 space space space space space space space space space space space rightwards double arrow space space space open vertical bar straight a with rightwards arrow on top close vertical bar space equals space 1 space equals space open vertical bar straight b with rightwards arrow on top close vertical bar

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