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amm1812
3 years ago
15

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

Mathematics
2 answers:
never [62]3 years ago
6 0

Answer:

Step-by-step 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)

Alchen [17]3 years ago
5 0
\bf \textit{unit vector for \underline{v}}\qquad v=\ \textless \ a,b\ \textgreater \ \implies \stackrel{unit~vector}{\cfrac{a}{\sqrt{a^2+b^2}}~,~\cfrac{b}{\sqrt{a^2+b^2}}}\\\\
-------------------------------\\\\
v=3i+j\implies v=\ \textless \ 3,1\ \textgreater \ \implies \stackrel{unit~vector}{\cfrac{3}{\sqrt{3^2+1^2}}~,~\cfrac{1}{\sqrt{3^2+1^2}}}
\\\\\\
\left( \cfrac{3}{\sqrt{10}}~,~\cfrac{1}{\sqrt{10}} \right)
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