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प्रश्न
Find the magnitude of two vectors `veca and vecb`, having the same magnitude and such that the angle between them is 60° and their scalar product is `1/2`.
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उत्तर १
We have, `theta = 60^circ, veca xx vecb = 1/2, |veca| = |vecb|`
If the angle between vectors `veca, vecb` is θ, then
Now, `costheta = (veca xx vecb)/(|veca||vecb|)`
`cos 60^circ = (1/2)/|veca|^2; 1/2 = 1/(2|veca|^2)`
`|veca|^2 = 1; |veca| = 1`
`|veca| = 1, |vecb| = 1`
उत्तर २
Magnitude of two vectors `veca and vecb` is same
`|veca| = |vecb|`
`veca.vecb = |veca| |vecb| costheta`, θ is the angle between `veca and vecb`
Given `theta = 60^\circ and veca.vecb = 1/2`
`veca.vecb = |veca| |vecb| costheta`
`veca.vecb = |veca| |veca| cos60^\circ`
`1/2 = |veca|^2 xx 1/2`
`|veca|^2 = 1`
`|veca| = +- 1`
Since magnitude of a vector is not negative
so `|veca| = 1`
`|veca| = |vecb| = 1`
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