In a triangle ABC,DandE are points on BCandAC, respectivley, such that BD=2DCandAE=3EC˙ Let P be the point of intersection of ADandBE˙ Find BP/PE using the vector method.
A vector has components p and 1 with respect to a rectangular Cartesian system. The axes are rotted through an angel αabout the origin the anticlockwise sense. Statement 1: IF the vector has component p+2and 1 with respect to the new system, then p=−1. Statement 2: Magnitude of the original vector and new vector remains the same.
Prove, by vector method or otherwise, that the point of intersection of the diagonals of a trapezium lies on the line passing through the midpoint of the parallel sides (you may assume that the trapezium is not a parallelogram).
Fined the unit vector in the direction of vector PQ , where P and Q are the points (1,2,3) and (4,5,6), respectively.
If the projections of vector a on x -, y - and z -axes are 2, 1 and 2 units ,respectively, find the angle at which vector a is inclined to the z -axis.
The vectors xi^+(x+1)j^+(x+2)k^,(x+3)i^+(x+4)j^+(x+5)k^and(x+6)i^+(x+7)j^+(x+8)k^ are coplanar if x is equal to a. 1 b. −3 c. 4 d. 0