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**TN17** Determine value of k when thehse are perpendicular:

[x,y,z] = [1+4s+kt, 2+2s+t, 7+2t]

and

[x,y,z] = [4,1,-1] + s[1,0,5] + t[0,-3,3]

I learned that in 2 and 3D, two lines are perpendicular only if, after solving for the t in front of the direction vector, x=x , y=y and z=z

My attempt was to Cross product the direction vecotrs in each of the equations, and then dot product those values to find k, since if they are perpend. then dot product=0

I'm not sure how they ended up with k = 31/3