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The parametric equations for a line L1 are as follows:

x = −3+6t
y = 2−9t
z = 4+3t

Let L2 be the line parallel to L1 and passing through the point (−2, 4, 5). Find the point P on L2 whose x-coordinate is 6.

6 = -2 + 6t

t = 4/3
y = 4 - 9(4/3) = -8
z = 5 + 3(4/3) = 9

Did you know?

Did you know that in mathematics, parametric equations can be used to describe the coordinates of points on a line? For example, given the parametric equations x = −3+6t, y = 2−9t, and z = 4+3t for line L1, we can determine the coordinates of any point on this line by substituting different values of t. Now, let's consider another line called L2, which is parallel to L1. To find a point on L2 whose x-coordinate is 6, we need to solve for the corresponding values of y and z. Additionally, we know that L2 passes through the point (−2, 4, 5). By setting the x-coordinate to 6 in the parametric equations, we can find the values of t, and then by substituting these values into the equations for y and z, we can determine the full coordinates of the point P.