If the vectors 3p+q;5p−3qand2p+q;4p−2q are pairs of mutually perpendicular vectors, then find the angle between vectors pandq˙
If i^−3j^+5k^ bisects the angle between a^and−i^+2j^+2k^,wherea^ is a unit vector, then a. a^=1051(41i^+88j^−40k^) b. a^=1051(41i^+88j^+40k^) c. a^=1051(−41i^+88j^−40k^) d. a^=1051(41i^−88j^−40k^)
A boat moves in still water with a velocity which is k times less than the river flow velocity. Find the angle to the stream direction at which the boat should be rowed to minimize drifting.
Let a,b,c be distinct non-negative numbers and the vectors ai^+aj^+ck^,i^+k^,ci^+cj^+bk^ lie in a plane, and then prove that the quadratic equation ax2+2cx+b=0 has equal roots.
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
Find the vector of magnitude 3, bisecting the angle between the vectors a=2i^+j^−k^ and b=i^−2j^+k^˙
A uni-modular tangent vector on the curve x=t2+2,y=4t−5,z=2t2−6t=2 is a. 31(2i^+2j^+k^) b. 31(i^−j^−k^) c. 61(2i^+j^+k^) d. 32(i^+j^+k^)