True False The line segment starting at the point 25 1 and

(True / False) The line segment starting at the point (2,5, - 1) and ending at (3,3,0) can be expressed with the equations x = 2 + t, y = 5 - 2t, z =- 1 +t for . (True / False) The parametric equations x = 3 - t, y = 1 + 2i, z = - t for describe a line segment that starts at the point (2,3, - 1) and ends at the point (4, - 1,1).

Solution

The line segment between two points P and Q can be parametrized as: (1-t)P + tQ

For the first part we have:

(1-t)(2,5,-1) + t(3,3,0) = (2-2t+3t , 5-5t+3t , t-1+0) = (2+t , 5-2t , -1+t)

x(t) = 2+t , y(t) = 5-2t , z(t) = -1+t

so the given equation is correct.

The second parametric equation is not correct, because if you put t = -1 into the equation we have:

x = 3-(-1) = 4

but the x-coordinate of the point (2,3,-1) is 2.