Consider the plane: -5x+8y-7z=-8. and the line:[x,y,z]^T=[-7,6,1]+s[6,7,4]^T. Find the smallest distance between the two.
I just have no idea how to do this question. I can find the normal vector to be the coefficients of the plane which is (-5,8,-7). P can be said as an arbitrary point when t=0. so, P=(-7,6-1). I can also find Po on the plane which can be (0,-1,0). I tried to do this question in terms of a projection by finding the vector V1. The answer i got is 84sqrt(138)/113. I dont believe this is correct at all. Any help is appreciated!