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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`
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Solution
If θ is the angle between any two vectors `bara` and `barb` and `|bara · barb| = |bara xx barb|` then θ is equal to `underlinebb(π/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`
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