Question

The angle made by \(\overrightarrow{r}=3\overrightarrow{i}+3\overrightarrow{j}\) with the x axis is

• A. 30°
• B. 60°
• C. 180°
• D. 90°
• E. 45°

Answer 1

Answer: (E)

The angle \( \theta \) made by a vector \( \vec{r} = x\hat{i} + y\hat{j} \) with the x-axis can be calculated using the formula: \[ \tan \theta = \frac{y}{x} \] Where: - \( x = 3 \), - \( y = 3 \). Substituting these values: \[ \tan \theta = \frac{3}{3} = 1 \] Therefore, \[ \theta = \tan^{-1}(1) = 45^\circ \] Thus, the angle made by the vector with the x-axis is \( 45^\circ \).

The correct option is (E) : \(45°\)

Answer 2

The vector is given as $\vec{r} = 3\hat{i} + 3\hat{j}$.  

To find the angle $\theta$ made with the x-axis, we use: 
$\tan \theta = \frac{\text{y-component}}{\text{x-component}} = \frac{3}{3} = 1$ 
$\theta = \tan^{-1}(1) = 45^\circ$ 

Correct answer: 45°