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 (-/3, 3). 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 :

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 the particle 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     \[\theta ={{60}^{o}}\]