The vectors $A B = 3 i - 2 j + 2 k$ and $B C = - i - 2 k$ are the adjacent sides of a parallelogram.
The angle between its diagonals is

π / 4

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π / 3

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3 π / 4

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2 π / 3

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Solution

The correct options are
B $3 π / 4$
C $π / 4$
The diagonals are given by $A B - B C = 4 i - 2 j + 4 k, A B + B C = 2 i - 2 j$
These vectors have magnitudes $6$ and $2 \sqrt{2}$ respectively, and their dot product is $12$ .
Therefore the angle between them is ${cos}^{- 1} \frac{12}{(6) (2 \sqrt{2})} = {cos}^{- 1} \frac{1}{\sqrt{2}} = \frac{π}{4}$
or $π$ minus this value i.e. $3 π / 4$

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

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The vectors $A B = 3 i - 2 j + 2 k$ and $B C = - i - 2 k$ are the adjacent sides of a parallelogram.
The angle between its diagonals is