In a triangle ABC, the sides AB and AC are represented by the vectors 3^i+^j+^k and ^i+2^j+^k respectively. Calculate the angle ∠ABC.
A
cos−1√511
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B
cos−1√611
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C
(90o−cos−1√511)
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D
(180o−cos−1√511)
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Solution
The correct option is Dcos−1√511 −−→AB=3^i+^j+^k −−→AC=^i+2^j+^k −−→CB=−−→AB−−−→AC 2^i−^j ∠ABC is angle between −−→AB and −−→CB −−→AB⋅−−→CB=|−−→AB||−−→CB|cosθ ⇒5=|√11||√5|cosθ cosθ=√5√11 θ=cos−1(√5√11).