Question

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

Answer 1

The cosines of the angles a vector makes with 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 ratio 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""_x^2 + A""_y^2 + A""_z^2)^(1/2)` ,

It is a general result that,

`alpha = cos theta = (A""_x)/(A""_x^2 + A""_y^2 + A""_z^2)^(1/2)`