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Question

Vertices of a triangle are represented by vectors A=^i2^j+2^k,B=2^i+^j^k and C=3^i^j+2^k. Then,

A
Length of side AB is 5 units.
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B
Length of side BC is of length 14 units.
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C
Angle between side AB & BC is θ=cos11419.
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D
Angle between side AB and BC is 30.
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Solution

The correct options are
B Length of side BC is of length 14 units.
C Angle between side AB & BC is θ=cos11419.

BA=OAOB
BA=^i3^j+3^k
BC=OCOB
BC=^i2^j+3^k
|BA|=19 and |BC|=14
BA.BC=|BA||BC|cosθcosθ=BA.BCBA.BC
cosθ=1+6+91419=1419

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