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Question
If θ is the angle between two vectors `veca` and `vecb`, then `veca . vecb >= 0` only when ______.
Options
`0 < θ < pi/2`
`0 ≤ θ ≤ pi/2`
`0 < θ < pi`
`0 ≤ θ ≤ pi`
Solution
If θ is the angle between two vectors `veca` and `vecb`, then `veca . vecb >= 0` only when `underline(0 ≤ θ ≤ pi/2)`.
Explanation:
Let θ be the angle between two vectors, `veca` and `vecb`.
Then, without loss of generality, `veca`,`vecb` are non zero vectors so that `|veca|,|vecb|` are positive
It is known that `veca × vecb = |veca||vecb|cosθ`
a × b ≥ 0
`|veca||vecb|cosθ≥0`
cosθ ≥ 0
`0 ≤ θ ≤ (π/2)`
So, a × b ≥ 0 when `0 ≤ θ ≤ (π/2).`
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