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Question

The vectors AB=3^i2^j+2^k and BC=^i2^k are the adjacent sides of a parallelogram. The angle between its diagonals is

A
π4
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B
π3
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C
3π4
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D
2π3
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Solution

The correct options are
A π4
C 3π4
The two diagonals are given by
ABBC=4^i2^j+4^k and AB+BC=2^i2^j

These vectors have magnitudes 6 and 22, respectively and their dot product is 12.

Therefore the angle between the is
cos112(6)(22)=cos112=π4 or ππ4=3π4

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