Question

The unit vector in the direction of \(3\vec{i}-9\vec{j}\) is

• A. \(\dfrac{3\vec{i}-9\vec{j}}{-6}\)
• B. \(\dfrac{3\vec{i}-9\vec{j}}{6}\)
• C. \(\dfrac{3\vec{i}-9\vec{j}}{\sqrt{90}}\)
• D. \(\dfrac{3\vec{i}-9\vec{j}}{\sqrt{70}}\)

Hint:

Unit vector = vector divided by its magnitude.

Answer 1

The Correct Option is C

Magnitude \(\|3\vec{i}-9\vec{j}\|=\sqrt{3^{2}+(-9)^{2}}=\sqrt{9+81}=\sqrt{90}\). Unit vector \(=\dfrac{1}{\|\cdot\|}\times\) vector \(=\dfrac{3\vec{i}-9\vec{j}}{\sqrt{90}}\) (which simplifies to \(\dfrac{\vec{i}-3\vec{j}}{\sqrt{10}}\)).