Question

What is the unit vector in the same direction as \[\vec{a}=\vec{i}-2\vec{j}\]?

Options

• \[\hat{a}=\frac{1}{\sqrt{5}}(\vec{i}-2\vec{j})\]

• \[\hat{a}=\sqrt{5}(\vec{i}-2\vec{j})\]

• \[\hat{a}=\frac{1}{\sqrt{5}}(\vec{i}+2\vec{j})\]

• \[\hat{a}=\frac{1}{5}(\vec{i}-2\vec{j})\]

Answer 1

A unit vector in the same direction is obtained by dividing the vector by its magnitude. Since \[|\vec{a}|=\sqrt{5}\], \[\hat{a}=\frac{1}{\sqrt{5}}(\vec{i}-2\vec{j})\].