1.

If vectors ` vec A , vec` B` and vec C`have magnitudes `5, 12 and 13 units and ` vec A + vec B =vec C`, find theangle between ` vec B and vec C`.

Answer» As ` vec A + vec B = vec C`
:. ` vec A = vec C - vec B`
Then ` vec A . Vec A =( vec C - vec B) .(vec C - vec B)`
`=vec C. vec C -2 vec C . Vec B + vev B . Vec B`
or `A^(2) =C^(2) -2 CB cos theta + B^(2)`
or `cos theta = (C^(32) + B^(2) -A%(2))/(2 C B)`
`=(13^(2) + 12^(2) 12^(2) -5^(2))/(2xx 13 xx 12)= 9288)/(312) =(12) /(13)`
`theta = cos ^(-1) (12 // 13)`.


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