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Question
The angle between two vectors `vec"a"` and `vec"b"` with magnitudes `sqrt(3)` and 4, respectively, and `vec"a" * vec"b" = 2sqrt(3)` is ______.
Options
`pi/6`
`pi/3`
`pi/2`
`(5pi)/2`
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Solution
The angle between two vectors `vec"a"` and `vec"b"` with magnitudes `sqrt(3)` and 4, respectively, and `vec"a" * vec"b" = 2sqrt(3)` is `pi/3`.
Explanation:
Here, given that `|vec"a"| = sqrt(3)`
`|vec"b"|` = 4
And `vec"a" * vec"b" = 2sqrt(3)`
∴ From scalar product, we know that
`vec"a" * vec"b" = |vec"a"||vec"b"| cos theta`
⇒ `2sqrt(3) = sqrt(3) * 4 cos theta`
⇒ `cos theta = (2sqrt(3))/(sqrt(3) * 4) = 1/2`
∴ `theta = pi/3`
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