AP EAMCET2016MathematicsVector Algebra

If a , b , c are non-zero vectors such that ( a b ) c = 1 3 | b || c | a , c a and is the angle between the vectors b and c , then is equal to

Options

A2 2 3
B1 3
C2 3
D2 3

Correct answer

A. 2 2 3

Step-by-step solution

Here, a, b and c are non-zero vectors C a c . a= 0 and is the angle between the vectors b and c . aligned & (a b) c= 1 3 |b||c| a & (c . a) b-(c . b) a= 1 3 |b||c| a & 0-(|c||b| ) a= 1 3 |b||c| a & =- 1 3 ^2 =- 1 9 & 1- ^2 = 1 9 ^2 =1- 1 9 = 8 9 & = 8 9 = 2 2 3 aligned

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