ABCD is a trapezium in which AB and CD are parallel. prove by vector methods that the midpoint of sides AB CD and the intersection of diagonals are collinear.

A body is rotating with an angular velocity of 2radians per second about the line joining (1, 2,3) and (2, 3,5) find the velocity of the particle of the body which is momentarily at (3, 5,6)

Show that: vectorPQ+vectorPR+ vectorPS +vectorTP+vectorUP = 4PQVector

Given that A×(B×C) = (A.C)B - ( A.B)C , deduce that (A×B)×C = (A.C)B - (B.C)A

the mean of 30 observations was 17 with sd2. later it was found that two of the observations were incorrect, which were recorded as 19vand 21.find the correct sd if the incorrect values are deleted and correct values 22 and 15 are included

Find the component of 2i +3j +k in the direction of 3i-j