Question

Which vector has magnitude \[7\] units in the direction of \[\vec{a}=\vec{i}-2\vec{j}\]?

Options

• \[\vec{v}=7\vec{i}-14\vec{j}\]

• \[\vec{v}=\frac{7}{\sqrt{5}}\vec{i}-\frac{14}{\sqrt{5}}\vec{j}\]

• \[\vec{v}=\frac{7}{\sqrt{5}}\vec{i}+\frac{14}{\sqrt{5}}\vec{j}\]

• \[\vec{v}=\frac{1}{\sqrt{5}}\vec{i}-\frac{2}{\sqrt{5}}\vec{j}\]

Answer 1

First use the unit vector \[\hat{a}=\frac{1}{\sqrt{5}}(\vec{i}-2\vec{j})\]. Multiplying it by \[7\] gives \[\vec{v}=\frac{7}{\sqrt{5}}\vec{i}-\frac{14}{\sqrt{5}}\vec{j}\].