Subjective Type

How do I find the angles between a vector and the $$x-$$ axis?

Solution

The cosines of the angles a vector makes the cartesian coordinate axes are the direction cosines.
If vector $$A$$ makes an angle $$\theta$$ with the $$x-$$axis, then it's direction cosine along $$x-$$axis is, $$\cos \theta= \alpha$$
If the direction also along the $$x-$$axis is $$A_x$$ and the other two direction ratios are $$A_y$$ and $$A_z$$, then the modulus of the vector is,
$$A=(A^2_x+ A^2_y+A^2_z)^{\dfrac{1}{2}}$$,
It is a general result that,
$$\alpha=\cos \theta=\dfrac{A_z}{(A^2_x+ A^2_y+A^2_z)^{\dfrac{1}{2}}}$$

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