Question

A vector $a$ has magnitude $5$ units and points north east and another vector $b$ has magnitude $5$ units and points north west. Then the magnitude of the vector $\left(a-b\right)$ is?

• A. $0$
• B. $5\sqrt{2}$
• C. $10$
• D. $25$

Answer 1

The correct option is B

$5\sqrt{2}$

Explanation for correct option:

Given, $\left|\overrightarrow{a}\right|=5,\left|\overrightarrow{b}\right|=5$ and angle between them is $90°$.

Apply formula for vector subtraction.$\left(\overrightarrow{a}-\overrightarrow{b}\right)=\sqrt{{\left|\overrightarrow{a}\right|}^2+{\left|\overrightarrow{b}\right|}^2-2\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \left(\theta \right)}$.

$\Rightarrow$$\left(\overrightarrow{a}-\overrightarrow{b}\right)=\sqrt{{\left(5\right)}^2+{\left(5\right)}^2-2\times 5\times 5\times \cos \left(90°\right)}$

$\Rightarrow$$\left(\overrightarrow{a}-\overrightarrow{b}\right)=\sqrt{50-0}$

$\Rightarrow$$\left(\overrightarrow{a}-\overrightarrow{b}\right)=5\sqrt{2}$

Hence, correct answer is option $\left(B\right)$.