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Question
Let the vectors `veca` and `vecb` be such that `|veca| = 3` and `|vecb| = sqrt2/3`, then `veca xx vecb` is a unit vector, if the angle between `veca` and `vecb` is ______.
Options
`pi/6`
`pi/4`
`pi/3`
`pi/2`
Solution
Let the vectors `veca` and `vecb` be such that `|veca| = 3` and `|vecb| = sqrt2/3`, then `veca xx vecb` is a unit vector, if the angle between `veca` and `vecb` is `underline(pi/4)`
Explanation:
`|veca| = 3, |vecb| = sqrt2/3`
`|veca xx vecb| = 1`
`|veca||vecb||sinthetahatn| = 1`
`|veca||vecb||sintheta| = 1`
`3 xx sqrt2/2 xx sintheta = 1`
`sintheta = 1/sqrt2`
`theta = pi/4`
The correct option is `pi/4`.
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