Parallelogram Law of Addition of Vectors

Author:R D Sharma
12th CBSE
IMPORTANT

Important Questions on Parallelogram Law of Addition of Vectors

EASY
IMPORTANT

ABCD is a parallelogram with AC and BD as diagonals. Then, AC-BD=

MEDIUM
IMPORTANT

The adjacent sides of a parallelogram are represented by the vectors a=i^+j^-k^ and  b=-2i^+j^+2k^. Find unit vectors parallel to the diagonals of the parallelogram.

MEDIUM
IMPORTANT

Show that the line segments joining the mid-points of opposite sides of a quadrilateral bisects each other.

MEDIUM
IMPORTANT

Show that the sum of three vectors determined by the medians of a triangle directed from the vertices is zero.

MEDIUM
IMPORTANT

ABCD is a parallelogram and P is the point of intersection of its diagonals. If O is the origin of reference, show that OA+OB+OC+OD=4OP.

MEDIUM
IMPORTANT

ABCD are four points in a plane and Q is the point of intersection of the lines joining the mid-points of AB and CD;BC and AD. Show that PA+PB+PC+PD=4PQ where P is any point.

HARD
IMPORTANT

Prove by vector method that the internal bisectors of the angles of a triangle are concurrent.

HARD
IMPORTANT

If a and b are two non-collinear vectors having the same initial point. What are the vectors represented by a+banda b.