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Question
If θ is the angle between any two vectors `bara` and `barb` and `|bara · barb| = |bara xx barb|` then θ is equal to ______.
Options
0
`π/4 or (3π)/4`
`π/2`
`pi or pi/6`
Solution
If θ is the angle between any two vectors `bara` and `barb` and `|bara · barb| = |bara xx barb|` then θ is equal to `bbπ/bb4 or bb(3π)/bb4`.
Explanation:
`|bara · barb| = |bara xx barb|`
We know:
`bara · barb = |bara||barb|` cosθ
`|bara xx barb| = |bara||barb|` sinθ
So,
`|cosθ| = |sinθ| ⇒ tanθ = ± 1 ⇒ θ = pi/4 or (3pi)/4`
`π/4 or (3π)/4`
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