question_answer

                A particle starting from the origin (0, 0) moves in a straight line in die (x, y) plane. Its coordinates at a later time are \[(\sqrt{3},\,\,3)\]. The path of the particle makes with the x-axis an angle of:                           

A)                 \[{{30}^{\text{o}}}\]

B)                 \[{{45}^{\text{o}}}\]

C)                 \[{{60}^{\text{o}}}\]

D)                 \[{{0}^{\text{o}}}\]

Correct Answer: C

Solution :

                Key Idea: Slope of the path of the particle gives the measure of angle required.                 Draw the situation as shown. OA represents the path of the particle starting from origin O(0, 0). Draw a perpendicular from point A to x-axis. Let path of makes an angle \[\theta \] with the x-axis, then                 \[\tan \theta =\] slope of line OA                                 \[=\frac{AB}{OB}=\frac{3}{\sqrt{3}}=\sqrt{3}\]                 or            \[\theta ={{60}^{o}}\]