1.

If ` veca +vecb +vecc =vec0, |veca| =3 , |vecb|=5 and |vecc| =7` , then the angle between ` veca and vecb` isA. `pi/2`B. ` pi/4`C. ` pi/6`D. ` pi/3`

Answer» Correct Answer - D
we have,
` veca + vecb +vecc= vec0`
` Rightarrow vecc = - ( veca + vecb)`
` Rightarrow |vecc| = |-(veca + vecb)|`
` Rightarrow |vecb|^(2) = |veca + vecb|^(2)`
` Rightarrow |vecc|^(2) =|veca|^(2) + |vecb|^(2) + 2( veca.vecb)`
` Rightarrow |veca|^(2) = |veca|^(2) +|vecb|^(2) + 2 |veca||vecb| cos theta`
where ` theta` is angle between ` veca and vecb`.
` Rightarrow 49 = 9 + 25 + 30 cos theta`
` Rightarrow 15= 30 cos theta Rightarrow cos theta = 1/2 Rightarrow theta = pi/3`


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