Write ` vec P Q+ vec R P+ vec Q R` in the simplified form.

In a quadrilateral P Q R S , vec P Q= vec a , vec Q R = vec b , vec S P= vec a- vec b ,M is the midpoint of vec Q Ra n dX is a point on S M such that S X=4/5S Mdot Prove that P ,Xa n dR are collinear.

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 .

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

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

Let vec a , vec ba n d vec c be three non-coplanar vectors and vec p , vec qa n d vec r the vectors defined by the relation vec p=( vec bxx vec c)/([ vec a vec b vec c]), vec q=( vec cxx vec a)/([ vec a vec b vec c])a n d vec r=( vec axx vec b)/([ vec a vec b vec c])dot Then the value of the expression ( vec a+ vec b)dot vec p+( vec b+ vec c)dot vec q+( vec c+ vec a)dot vec r is a. 0 b. 1 c. 2 d. 3

A B C D are four points in a plane and Q is the point of intersection of the lines joining the mid-points of A B and C D ; B C and A Ddot Show that vec P A+ vec P B+ vec P C+ vec P D=4 vec P Q , where P is any point.

A B C D are four points in a plane and Q is the point of intersection of the lines joining the mid-points of A B and C D ; B C and A Ddot Show that vec P A+ vec P B+ vec P C+ vec P D=4 vec P Q , where P is any point.

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

If |vec(P) + vec(Q)| = |vec(P) - vec(Q)| , find the angle between vec(P) and vec(Q) .

vec a , vec b , vec c are three coplanar unit vectors such that vec a+ vec b+ vec c=0. If three vectors vec p , vec q ,a n d vec r are parallel to vec a , vec b ,a n d vec c , respectively, and have integral but different magnitudes, then among the following options, | vec p+ vec q+ vec r| can take a value equal to a. 1 b. 0 c. sqrt(3) d. 2