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

May 30, 2015

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, $C o s \theta = \alpha$.

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,

$A = {\left(A {\text{_x^2 + A""_y^2 + A}}_{z}^{2}\right)}^{\frac{1}{2}}$ ,

It is a general result that,

$\alpha = \cos \theta = {\left(A {\text{_x)/(A""_x^2 + A""_y^2 + A}}_{z}^{2}\right)}^{\frac{1}{2}}$