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Question
If the angle between `veca` and `vecb` is `π/3` and `|veca xx vecb| = 3sqrt(3)`, then the value of `veca.vecb` is ______.
Options
9
3
`1/9`
`1/3`
Solution
If the angle between `veca` and `vecb` is `π/3` and `|veca xx vecb| = 3sqrt(3)`, then the value of `veca.vecb` is 3.
Explanation:
∵ `veca xx vecb = |veca|.|vecb| sin θ`
`\implies |veca|.|vecb| sin π/3 = 3sqrt(3)` ...`[∵ θ = π/3]`
`\implies |veca|.|vecb|. sqrt(3)/2 = 3sqrt(3)`
`\implies |veca|.|vecb|` = 6 ...(i)
Now `veca.vecb = |veca|.|vecb| cos θ`
`veca.vecb = 6 . cos π/3` ...[From (i)]
= `6 . 1/2`
`veca.vecb` = 3.
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