How do I find all the vectors of V when U=(-1,3,2) and W=(1,1,-1) and what geometric figure does the outcome of V from?

Question

U x V = W
Can you explain in detail how I get there ?

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Answer 1 · 2018-01-01T07:38:24

The solution is #=O/#

Let #vecV=(x,y,z)#

The cross product of

#vecU xx vecV=|(hati,hatj,hatk),(-1,3,2),(x,y,z)|#

#=veci(3z-2y)-vecj(-z-2x)+veck(-y-3x)#

But #vecUxxvecV=vecW#

and #vecW=(1,1,-1)#

Therefore,

#-2y+3z=1#.......#(1)#

#2x+z=1#...........#(2)#

#-3x-y=-1#.............#(3)#

Solving for #(x,y,z)# in equations #(1)#, #(2)# and #(3)#

We get

#3x+y=2# and

#3x+y=1#

The determinant of the system of equations #(1)#, #(2)#, and #(3)# is

#|(0,-2,3),(2,0,1),(-3,-1,0)|=0#

The solution is #=O/#