question_answer

Locus of the point P, for which \[\overrightarrow{OP}\] represents a vector with direction cosine \[\cos \,\,\alpha =\frac{1}{2}\] (where O is the origin) is

A) a circle parallel to the y-z plane with centre on the x-axis

B) a cone concentric with the positive x-axis having vertex at the origin and the slant height equal to the magnitude of the vector

C) a ray emanating from the origin and making an angle of \[60{}^\circ \]with the x-axis

D) a disc parallel to the y-z plane with centre on the x-axis and radius equal to \[\left| \overrightarrow{OP} \right|\] sin 60°

Correct Answer: B

Solution :

[b] From the diagram, it is obvious that locus is a cone concentric with the positive x-axis having vertex at the origin and the slant height equal to the magnitude of the vector.