Answer
$59.5^{ \circ}$
Work Step by Step
The formula to calculate the angle between the vector v and the x-axis is:
$ \theta = \cos ^{-1} (\dfrac{v_x}{|v|})$
Here, $v=\lt 3,-5,1 \gt$
$|v|=\sqrt{3^2+(-5)^2+(1)^2}= \sqrt {35}$
Thus, $ \theta = \cos ^{-1} (\dfrac{v_x}{|v|})=\cos ^{-1} (\dfrac{3}{ \sqrt {35}})$
or, $ \theta =59.5^{ \circ}$
