Find the unit vector in the direction of the vector a=i^+j^+2k^
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).
If ∣∣a+b∣∣<∣∣a−b∣∣, then the angle between aandb can lie in the interval a. (π/2,π/2) b. (0,π) c. (π/2,3π/2) d. (0,2π)
If b is a vector whose initial point divides thejoin of 5i^and5j^ in the ratio k:1 and whose terminal point is the origin and ∣∣b∣∣≤37,thenk lies in the interval a. [−6,−1/6] b. (−∞,−6]∪[−1/6,∞) c. [0,6] d. none of these
The points with position vectors 60i+3j,40i−8j,ai−52j are collinear if a. a=−40 b. a=40 c. a=20 d. none of these
If r1,r2,r3 are the position vectors of the collinear points and scalar pandq exist such that r3=pr1+qr2, then show that p+q=1.
Column I, Column II Collinear vectors, p.a Coinitial vectors, q. b Equal vectors, r. c Unlike vectors (same intitial point), s. d
Show that the points A(1,−2,−8),B(5,0,−2)andC(1,3,7) are collinear, and find the ratio in which B divides AC˙