`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 (vecp) and Q (vecq) are the position vectors of two fixed points and R(vecr) is the postion vector of a variable point. If R moves such that (vecr-vecp)xx (vecr-vecq)=vec0 then the locus of R is

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.

Write the position vector of the point where the line vec r= vec a+lambda vec b meets the plane vec r dot (vec n)=0.

If vec p is a unit vector and ( vec x-\ vec p).( vec x+\ vec p)=80 , then find | vec x|

The position vectors of P and Q are respectively vec a and vec b . If R is a point on vec(PQ) such that vec(PR) = 5 vec(PQ), then the position vector of R, is

If P ,Q and R are three collinear points such that vec P Q= vec a and vec Q R = vec bdot Find the vector vec P R .

P and Q are two points with position vectors 3 vec a-2 vec b and vec a+ vec b respectively. Write the position vector of a point R which divides the line segment PQ in the ratio 2:1 externally.

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2\ vec a+ vec b) and ( vec a-\ 3 vec b) respectively, externally in the ratio 1:2.Also, show that P is the mid-point of the line segment R Qdot

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vec rxx veca is equal to a. [ vec r vec a vec b] vec b-( vec r. vec b)( vec bxx vec a) b. [ vec r vec a vec b]( vec a+ vec b) c. [ vec r vec a vec b] vec a-( vec r. vec a) vec axx vec b d. none of these