If ` vec r_1, vec r_2, vec r_3` are the position vectors of the collinear points and scalar `p a n d q` exist such that ` vec r_3=p vec r_1+q vec r_2,` then show that `p+q=1.`

If vec r_1, vec r_2, vec r_3 are the position vectors off thee collinear points and scalar pa n dq exist such that vec r_3=p vec r_1+q vec r_2, then show that p+q=1.

If vec r_1, vec r_2, vec r_3 are the position vectors of the collinear points and scalar p a n d q exist such that vec r_1=p vec r_2+q vec r_3, then show that p+q=1.

If vec r_(1),vec r_(2),vec r_(3) are the position vectors of the collinear points and scalar pandq exist such that vec r_(3)=pvec r_(1)+qvec r_(2), then show that p+q=1.

Let OP,OQ, OR are three edges of a regular tetrahedron of edge length a . If vec p , vec q and vec r are the position vectors of the points P,Q and R & O is the origin then |vec p timesvec q+vec q timesvec r+vec r timesvec p| is equal to

P(vec p) and Q(vec q) are the position vectors of two fixed points and R(vec r) is the position vectorvariable point.If R moves such that (vec r-vec p)xx(vec r-vec q)=0 then the locus of R is

P(vec p) and Q(vec q) are the position vectors of two fixed points and R(vec r) is the position vectorvariable point. If R moves such that (vec r-vec p)xx(vec r -vec q)=0 then the locus of R is

P(vec p) and Q(vec q) are the position vectors of two fixed points and R(vec r) is the position vectorvariable point. If R moves such that (vec r-vec p)xx(vec r -vec q)=0 then the locus of R is

P(vec p) and Q(vec q) are the position vectors of two fixed points and R(vec r) is the position vectorvariable point. If R moves such that (vec r-vec p)xx(vec r -vec q)=0 then the locus of R is

P(vec p) and Q(vec q) are the position vectors of two fixed points and R(vec r) is the position vectorvariable point. If R moves such that (vec r-vec p)xx(vec r -vec q)=0 then the locus of R is

If vec(PO) + vec(OQ) = vec(QO) + vec(OR) prove that the points P,Q,R are collinear .