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If veca+vecb+vecc=vec0, |veca| = 3, |vec...

If `veca+vecb+vecc=vec0, |veca| = 3, |vecb| = 5, |vecc| = 7`, then angle between `veca` and `vecb` is : a. `(pi)/(2)` b. `(pi)/(3)` c. `(pi)/4` d. `(pi)/(6)`

A

`pi/2`

B

` pi/4`

C

` pi/6`

D

` pi/3`

Text Solution

Verified by Experts

The correct Answer is:
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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