VECTOR PROBLEM The cross product of the normal vectors to two planes is a vector that points in the direction of the line of intersection of the planes. Find a particular equation of the plane containing (-3, 6, 5) and normal to the line of intersection of the planes 3x + 5y + 4z = -13 and 6x - 2y + 7z = 8 Can someone guide me through it?

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Since no one is responding, let me start with a simpler question. Would the cross product be a vector that is perpendicular to the line it is pointing towards? If so, it would be a bit simpler...

Well finding the cross product is pretty simple. (3,5,4)x(6,-2,7)=(43,3,-36) This is the direction the line of intersection is pointing in. I'm just confused about what they mean by a plane that is normal to the line of intersection. Does the plane pass through the line? Is the normal perpendicular to the line?

Here's a cute little graph I made, it might help :P Blue lines are normals to planes and red line is cross product.

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