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JEE Previous Year Question

$If α is the angle between two vector p = 3 i + 4 j - k and q = 2 i - j + k, then sin (α) =$

Topic: JEE PYQ

Answer: C. Full step-by-step solution below.

A $\frac{145}{156}$
B $\frac{135}{156}$
C $\frac{155}{156}$
D $\frac{165}{156}$

Correct answer: C

Solution

(c) Angle between vectors p and q . sin α = \frac{| p \times q |}{| p | | q |} = \frac{( 4 - 1 ) ^{2} + ( - 3 - 2 ) ^{2} + ( - 3 - 8 ) ^{2}}{9 + 16 + 1 4 + 1 + 1} = \frac{9 + 25 + 121}{26 6} = \frac{155}{156}

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