Can a vector have direction angles 45º, 60º, 120º? - Vidyadip

Question

Can a vector have direction angles 45º, 60º, 120º?

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Answer

Yes,
Let a vector makes an angle $\alpha=45^{\circ},\ \beta=60^{\circ},\ \gamma=120^{\circ}$ with OX, OY, OZ respectively.
Let l, m, n be the direction cosines of the vector. Then,
$\text{l}=\cos45^{\circ}=\frac{1}{\sqrt{2}}$
$\text{m}=\cos60^{\circ}=\frac{1}2$
$\text{n}=\cos120^{\circ}=-\frac{1}2$
So,
$\text{l}^2+\text{m}^2+\text{n}^2$
$=\frac{1}2+\frac{1}4+\frac{1}4$
$=1$
Since, the vector has direction cosines such that $\text{l}^2+\text{m}^2+\text{n}^2=1$
Hence, a vector can have direction angles 45º, 60º, 120º

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