Question

the unit vector of v+3i-j

Answer 1

v=3i-j

Answer 2

divide v by its "length" or magnitude
if v = (3,-1) (and it does)
|v|^2 = \( v \cdot v \) = 9+1 = 10
and |v|=\(\sqrt{10}\)

the unit length vector in the same direction as \(\mathbf{v}\) will be
\[ \left(\frac{3}{\sqrt{10}}, -\frac{1}{\sqrt{10}}\right) \]
or using i, j notation
\[ \frac{3}{\sqrt{10}}\mathbf{i} -\frac{1}{\sqrt{10}}\mathbf{j} \]