Question

Find the unit vector that has the same direction as the vector v. v = 3i + j

(answer choices are pictured below)

Answer 1

`\bf \textit{unit vector for \underline{v}}\qquad v=\ \textless \ a,b\ \textgreater \ \implies \stackrel{unit~vector}{\cfrac{a}{√(a^2+b^2)}~,~\cfrac{b}{√(a^2+b^2)}}\\\\ -------------------------------\\\\ v=3i+j\implies v=\ \textless \ 3,1\ \textgreater \ \implies \stackrel{unit~vector}{\cfrac{3}{√(3^2+1^2)}~,~\cfrac{1}{√(3^2+1^2)}} \\\\\\ \left( \cfrac{3}{√(10)}~,~\cfrac{1}{√(10)} \right)`

Answer 2

Explanation:

Given is a vector v =3i+j

To find unit vector in the direction of v:

Since direction is the same as v we need not change the coefficients of i and j

But magnitude must be changed to 1.

Calculate the magnitude of vector v

|v|=\sqrt {3^2+1^2} =\sqrt{10}

TO make magnitude to 1 we divide the vector by magnitude

Hence unit vector

= \frac{1}{\sqrt{10}}(3i+j)