If p=2i-j and q=3i+4j, find a vector which has the magnitude of p and Is parallel to q?

Answers (1)

\begin{array}{ll} p=2 i-j & \Rightarrow |p|=\sqrt{{2}^{2}+(-1)^{2}}=\sqrt{5} \\ q=3 i+4 j & \Rightarrow |q|=\sqrt{{3}^{2}+4^{2}}=5 \end{array}

So for finding vector having magnitude = 1 and direction same as q (i.e parallel to q)

we have to find unit vector along with q

i.e \hat{q}=\frac{\vec{q}}{|\vec{q}|}

Now find a vector which has the magnitude of p and Is parallel to q

we have multiply magnitude of p with a unit vector of q

i.e vector needed=|\vec{p}|\hat{q}=|\vec{p}|\frac{\vec{q}}{|\vec{q}|}= (\sqrt{5})*\frac{(3\vec{i}+4\vec{j})}{5}=\frac{(3\vec{i}+4\vec{j})}{\sqrt{5}}

 

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