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 \[(\sqrt{3},3).\] The path of the particle makes with the \[x-\]axis an angle of

A) \[{{30}^{0}}\]             

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

C) \[{{60}^{o}}\]              

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

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