Direction Numbers of Line of Intersection of 2 Planes

Direction Numbers for Line of Intersection of 2 Planes:

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Find the direction numbers for the line of intersection, L, of

plane P1: 2x - y + 3z = 4 and

plane P2: x + 3y -4z = 2

The line of intersection, L, lies in both planes, and hence is perpendicular to the normal vectors of both planes. The cross product, n₁ ´ n₂, is also perpendicular to n₁ and n₂, so it can be used as a reference vector in the direction of the line.

From the equations, we can determine the normal vectors:

n₁ = 2i - j + 3k, and

n₂ = i + 3j - 4k.

Now we form the cross product:

_{=-5i + 11j + 7k

Hence the direction numbers are -5, 11, 7.

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Email to John Taylor

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