For given vectors, a=2i^−j^+2k^ and b=−i^+j^−k^ find the unit vector in the direction of the vector a+b.
Vectors aandb are non-collinear. Find for what value of n vectors c=(n−2)a+bandd=(2n+1)a−b are collinear?
ABCD is a tetrahedron and O is any point. If the lines joining O to the vrticfes meet the opposite faces at P,Q,RandS, prove that APOP+BQOQ+CROR+DSOS=1.
A man travelling towards east at 8km/h finds that the wind seems to blow directly from the north On doubling the speed, he finds that it appears to come from the north-east. Find the velocity of the wind.
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