The distance between the skew linesr=OP+t d_1andr=OQ+s d_2is |Proj(PQonton)| or |PQ.n|/|n| wherern=d_1xd_2.

Find the distance between the lines x=6, y=-4-t, z=t, and x = -2s, y=5, z=3+s.

Bolded = vectors (arrow on top)

My answer is as follows:

x=6

y=-4-t

z=t

therefore in parametric eqtn form

(x-6)/0

(y+4)/-1

z/1

d_1 = (0,-1,1)

x/-2

(y-5)/0

(z-3)/1

d_2=(-2,0,1)

PQ=d=(-2,1,0)

(-2,1,0) . (-1,0,-2)

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sqrt5

final answer

1/sqrt5

is this correct??

please let me know.

thanks!