And are the position vector of two fixed points and is the position vector of a…

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

P(p)

and

Q(q)

are the position vector of two fixed points and

R(r)

is the position vector of a variable point. If

R

moves such that

(r - p) \times (r - q) = 0

, then the locus of

R

is (1) a plane containing the origin

O

and parallel to two non-collinear vector

OP

and

OQ

. (2) the surface of a sphere described on

PQ

as its diameter. (3) a line passing through the points

P

and

Q

. (4) a set of lines parallel to the line

PQ