Question

Find parametric equations for the line described below. The line through the points P(−1,−1,5) and Q(4,6, −4) x=t−5,y=t−7,z=5t+9x=t+5,y=t+7,z=5t−9x=5t+1,y=7t+1,z=−9t−5x=5t−1,y=7t−1,z=−9t+5​

Answer 1

To find the parametric equations for the line passing through points P(-1, -1, 5) and Q(4, 6, -4), you can use the differences of the coordinates to determine the direction vector. Then, set up the parametric equations using the point-slope form and substituting the coordinates of point P.

Step-by-step explanation:

To find the parametric equations for the line passing through points P(-1, -1, 5) and Q(4, 6, -4), we can take the differences of the x, y, and z coordinates of the two points to determine the direction vector of the line. The direction vector is D = (4 - (-1), 6 - (-1), -4 - 5) = (5, 7, -9). Now, we can set up the parametric equations using the point-slope form and substituting the coordinates of point P:

x = -1 + 5t,

y = -1 + 7t,

z = 5 + (-9)t.