Question

Vector b~ has x, y, and z components of 4.4, 9.6, and 5 units, respectively. what is the angle between b~ and the x-axis?

Answer 1

The simplest vector you can take along the x-axis is $\mathbf v=langle1,0,0\rangle$.

Now,

$\mathbf b\cdot\mathbf v=\|\mathbf b\|\|\mathbf v\|\cos\theta$

where $\theta$ is the angle between the two vectors. You have

$\mathbf b\cdot\mathbf v=\langle4.4,9.6,5\rangle\cdot\langle1,0,0\rangle=4.4$
$\|\mathbf b\|=\sqrt{4.4^2+9.6^2+5^2}\approx11.68$
$\|\mathbf v\|=\sqrt{1^2+0^2+0^2}=1$

so that

$4.4=11.68\cos\theta\implies\cos\theta=0.3767\implies \theta\approx67.87^\circ$