The tangents at the points P(ap2, 2ap) and Q(aq2, 2aq) on the parabola y2 = 4ax
intersect at the point R. Given that the tangent at P is perpendicular to the chord
OQ, where O is the origin, find the equation of the locus of R as p varies.

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 = 4PQ

Vector

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