Question

Let L7​ te the ine paising through the points Q1​−(2,1,−3) and Q2​−(−2,−1,1) and let L2​ be the lne passing trrough sve point p1​−(−4,−6,3) with direction vector If [2,−1,−2]T. Desermine whether L4​ and L2​ mersect. If so, find the point of intesection Q. KSelect one?

Answer 1

To find if lines L1 and L2 intersect, we solve for the parameters t and s in the parametric equations of the lines that would result in the same point Q. If there is a solution, it is the intersection point.

Step-by-step explanation:

To determine whether two lines intersect, we need to solve a system of equations that represents each line. The line L1 passing through points Q1​−(2,1,−3) and Q2​−(−2,−1,1) can be expressed as a parametric equation. To find this, we can get the direction vector d1 by subtracting the coordinates of Q1 from Q2. The line L2 is given to be passing through the point P1​−(−4,−6,3) with direction vector d2 = [2,−1,−2]T. The equations for L1 and L2 are:

L1: r = Q1 + t ∗ d1
L2: r = P1 + s ∗ d2

Where t and s are parameters. We solve for t and s such that r is the same point on both lines, which would be point Q, the point of intersection. If there are no solutions, the lines do not intersect. If there is one solution, it indicates the point at which they intersect.