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

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