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.

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

Let vec r_1, vec r_2, vec r_3, , vec r_n be the position vectors of points P_1,P_2, P_3 ,P_n relative to the origin Odot If the vector equation a_1 vec r_1+a_2 vec r_2++a_n vec r_n=0 hold, then a similar equation will also hold w.r.t. to any other origin provided a. a_1+a_2+dot+a_n=n b. a_1+a_2+dot+a_n=1 c. a_1+a_2+dot+a_n=0 d. a_1=a_2=a_3dot+a_n=0

If vec a and vec b are two given vectors and k is any scalar, then find the vector vec r satisfying vec rxx vec a+k vec r= vec b .

If vec P O+ vec O Q= vec Q O+ vec O R , show that the point, P ,Q ,R are collinear.

vec a , vec b ,a n d vec c are three unit vectors and every two are inclined to each other at an angel cos^(-1)(3//5)dot If vec axx vec b=p vec a+q vec b+r vec c ,w h e r ep ,q ,r are scalars, then find the value of qdot

If vec ra n d vec s are non-zero constant vectors and the scalar b is chosen such that | vec r+b vec s| is minimum, then the value of |b vec s|^2+| vec r+b vec s|^2 is equal to a. 2| vec r|^2 b. | vec r|^2//2 c. 3| vec r""|^2 d. |r|^2

Write the equation of the plane containing the lines vec r= vec a+lambda vec b\ a n d\ vec r= vec a+mu vec c

If vec(P) xx vec(Q) =vec(R ) , then which of the following statements is not true?