`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 veca and vecb are position vectors of A and B respectively, then the position vector of a point C in vec(AB) produced such that vec(AC) =2015 vec(AB) 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.

ABCD is a rectangle with A as the origin. vec b and vec d are the position vectors of B and D respectively. (i) What is the position vector of C? (ii) If P, Q, R and S are midpoints of sides of AB, BC, CD and DA respectively, find the position vector of P, Q, R,S,

If for two vectors vec(A) and vec(B), vec(A) xx vec(B) = 0 then the vectors are :

If for two vectors vec(A) and vec(B), vec(A) xx vec(B) = 0 then the vectors are :

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) externally in the ratio 1 :2. Also, show that P is the midpoint of the line segment RQ.

If vec a and vec b are orthogonal unit vectors, then for a vector vec r noncoplanar with vec a and vec b , vector rxxa 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

Let vec a=- hat i- hat k , vec b=- hat i+ hat ja n d vec c= hat i+2 hat j+3 hat k be three given vectors. If vec r is a vector such that vec rxx vec b= vec cxx vec b and vec r . vec a=0, then find the value of vec r . vec bdot

If vec a , vec b are two non-collinear vectors, prove that the points with position vectors vec a+ vec b , vec a- vec b and vec a+lambda vec b are collinear for all real values of lambdadot

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