Question

A person pushes a box kept on a horizontal surface with a force of $100N$. In unit vector notation, the force can be expressed as

• A. $100(\hat{i}+\hat{j})$
• B. $100(\hat{i}-\hat{j})$
• C. $50\sqrt{2}(\hat{i}-\hat{j})$
• D. $50\sqrt{2}(\hat{i}+\hat{j})$

Answer 1

The correct option is C $50\sqrt{2}(\hat{i}-\hat{j})$

Resolving force of magnitude $F$ into components

$\overrightarrow{F}=F\cos {45}^{\circ }\hat{i}+F\sin {45}^{\circ }(-\hat{j})$
$\overrightarrow{F}=50\sqrt{2}\hat{i}-50\sqrt{2}\hat{j}N$
$\overrightarrow{F}=50\sqrt{2}(\hat{i}-\hat{j})N$