question_answer

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

A) \[30{}^\circ \]                                   

B) \[45{}^\circ \]

C) \[60{}^\circ \]                                   

D) \[0{}^\circ \]

Correct Answer: C

Solution :

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 the particle makes an angle 0with the x-axis, then \[\tan  \theta = slope of line\,\,OA\] \[=\frac{AB}{OB}=\frac{3}{\sqrt{3}}=\sqrt{3}\] \[or \,\theta =60{}^\circ \]