Find points P,Q which are closest possible with P lying on the line
x = 7−2t, y = −2−7t, z = 1+5t
and Q lying on the line
x = −60−9t, y = −428+3t, z = −526−2t
So I was a little confused on how to draw the lines in terms of t. I was also not sure how exactly we could use these equations to find specific coordinates, especially when the equations are already written in terms of x, y and z.
Any help?
the two lines are given by $$x=7-2t,y=-2-7t,z=1+5t$$ and $$x=-60-7s,y=-428+3s,z=-526-2s$$ so we have the distance by $$d=\sqrt{(x_P-x_Q)^2+(y_p-y_Q)^2+(z_P-z_q)^2}$$ plugging the equations above in this formula we get $$d=\sqrt{(7-2t+60+9s)^2+(-2-7t+428-3s)^2+(1+5t+526+2s)^2}$$ this is a function in $s,t$ and you can optimize this. The result is $s=-5,t=7$