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Question
If `|veca xx vecb| = sqrt(3)` and `veca.vecb` = – 3, then angle between `veca` and `vecb` is ______.
Options
`(2π)/3`
`π/6`
`π/3`
`(5π)/6`
Solution
If `|veca xx vecb| = sqrt(3)` and `veca.vecb` = – 3, then angle between `veca` and `vecb` is `underlinebb((5π)/6)`.
Explanation:
Given,
`|veca xx vecb| = sqrt(3)` and `veca.vecb` = – 3
Then `|veca||vecb| sin θ = sqrt(3)` ...(i)
and `|veca||vecb| cos θ` = – 3 ...(ii)
On dividing (i) by (ii), we get
`sinθ/cosθ = sqrt(3)/-3 = (-1)/sqrt(3)`
`\implies` tan θ = `- tan (π/6)`
`\implies` θ = `π - π/6`
= `(5π)/6`
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