If either a=0and b=0then a×b=0. Is Is the converse true? Justify your answer with an example.
If the vectors c,a=xi^+yj^+zk^andb=j^ are such that a,candb form a right-handed system, then find ⋅
Let a=i−k,b=xi+j+(1−x)k and c=yi+xj+(1+x−y)k . Then [abc] depends on (A) only x (B) only y (C) Neither x nor y (D) both x and y
If the vectors 3p+q;5p−3qand2p+q;4p−2q are pairs of mutually perpendicular vectors, then find the angle between vectors pandq˙
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.
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˙