Question

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

• A. A circle parallel to $y$ z plane with centre on the $x$-axis
• B. a cone concentric with 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 $x$-axis
• D. a disc parallel to yz plane with centre on $x-$ axis \& radius equal to $|\overrightarrow{OP}|\sin 60^{\circ }$

Answer 1

Answer: (B)

Correct answer is (b) a cone concentric with positive $x$ - axis having vertex at the origin and the slant height equal to the magnitude of the vector