Question

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 $60^{\circ}$

Answer 1

Answer: (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.