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Angle between vectors veca and vecb " ...

Angle between vectors ` veca and vecb " where " veca,vecb and vecc` are unit vectors satisfying ` veca + vecb + sqrt3 vecc = vec0` is

A

` pi/6`

B

`pi/4`

C

`pi/3`

D

` pi/2`

Text Solution

Verified by Experts

The correct Answer is:
C
we have,
` veca + vecb + sqrt3 vecc = vec0`
` Rightarrow veca | vecb = sqrt3 vecc`
` Rightarrow |veca + vecb| = sqrt3 |vecc|`
` Rightarrow |veca + vecb|^(2) =3 |vecc|^(2) `
` Rightarrow |veca|^(2) +|vecb|^(2) + 2|veca||vecb| cos theta =3 |veca|^(2) `
where ` theta ` is the angle between ` veca and vecb` .
` Rightarrow 1 +1 + 2 cos theta =3 Rightarrow = 1/2 Rightarrow theta = pi/3`
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