Originally posted by: dighn
Originally posted by: andrey
Can anyone give me a hint here...
1. If v cross w = 2i-3j+5k, and v cross w = 3, find tangent Q, where Q is the angle between vectors v and w
2. Find vector which is parallel to the intersection of two planes: 2x-3y+5z=2 and 4x+y-3z=7
1.
i assume u mean v dot w = 3 b/c what u said makes no sense at all
magnitude wise:
cross: vwsin(Q)=mag(result)=sqrt(4+9+25) = sqrt(38)
dot: vwcos(Q) = 3
divide the top two lines you get
sin(q)/cos(q) = sqrt(38)/3
but sin(q)/cos(q) = tan(q)
u have ur answer
2.
whatever the intersection is, the vector must be on both planes ie must be normal to the plane normal vectors
the plane normal vectors are (2,-3,5) and (4,1,-3)
cross (2,-3,5) and (4,1,-3) and u have ur answer