Question

Show that line →r=(^i+^j−^k)+λ(3^i−^j) and →r=(4^i−^k)+μ(2^i+3^k) intersect. Also find their point of intersection.

Answer 1

To show that the two lines intersect, we need to find the values of λ and μ for which the two lines have the same position vector. The point of intersection is (-2, 0, -1).

Step-by-step explanation:

To show that the two lines intersect, we need to find the values of λ and μ for which the two lines have the same position vector. We can set the x, y, and z components of the position vectors equal to each other and solve for λ and μ.

For the x component: 1 + 3λ = 4 + 2μ
For the y component: 1 - λ = 0
For the z component: -1 - λ = 0

Solving these equations, we find that λ = -1 and μ = -1. Substituting these values back into either of the original equations will give us the point of intersection. Plugging λ = -1 into the first equation, we get:

x = 1 + 3(-1) = -2

So, the point of intersection is (-2, 0, -1).