Find parametric equations of the line passing through the po

Solution

The parametric equation of the line is:

t(1,2,3) + (1-t)(3,5,7) =

(t,2t,3t)+(3-3t , 5-5t , 7-7t) =

(3-2t , 5-3t , 7-4t)

To find the shortest distance we have:

d(t) = (3-2t-0)² + (5-3t-0)² + (7-4t-0)²

d\'(t) = -4(3-2t) - 6(5-3t) - 8(7-4t) = 0

-12+8t-30+18t-56+32t = 0

58t = 98

t = 98/58 = 49/29

So the shortest distance is:

d(49/29) = ((3-2*49/29)² + (5-3*49/29)² + (7-4*49/29)²) = (6/29) = 0.4549