If the vector product of a constant vector ` vec O A` with a variable vector ` vec O B` in a fixed plane `O A B` be a constant vector, then the locus of `B` is a straight line perpendicular to ` vec O A` b. a circle with centre `O` and radius equal to `| vec O A|` c. a straight line parallel to ` vec O A` d. none of these

Options

A. a straight line perpendicular to `vec(OA)`
B. a circle with centre O and radius equal to `|vec(OA)|`
C. a striaght line parallel to `vec(OA)`
D. none of these

Answer

c

Explanation

`|veca xx vecr| = |vecc|`
Triangles on the same base and between the same parallel will have the same area.