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)  \[30{}^\circ \]                  

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