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Question
If θ is the angle between any two vectors `veca` and `vecb,` then `|veca.vecb| = |veca xx vecb|` when θ is equal to ______.
Options
0
`pi/4`
`pi/2`
π
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Solution
If θ is the angle between any two vectors `veca` and `vecb,` then `|veca.vecb| = |veca xx vecb|` when θ is equal to `underline(pi/4)`.
Explanation:
Let θ be the angle between two vectors `veca` and `vecb`.
Then, without loss of generally, `veca` and `vecb` are non-zero vectors, so that `|veca∣and |vecb|` are positive.
`|veca.vecb| = |veca xx vecb|`
⇒ `|veca||vecb|cosθ = |veca||vecb|`sinθ
⇒ cosθ = sinθ [`veca` and `vecb` are positive]
⇒ tanθ = 1
⇒ θ = `pi/4`
Hence, `|veca.vecb| = |veca xx vecb|` when θ is equal to `pi/4`.
The correct answer is `pi/4`.
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