Hello everyone! I truly hope someone can explain this question out to help me out! It's been 2 hours and still no luck! Any help is truly appreciated!

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Let A1x+B1y+C1z+D1 = 0 and A2x+B2y+C2z+D2=0 be 2 non-parallel planes in space. Show that for any fixed k,

A1x+B1y+C1z+D1+ k(A2x+B2y+C2z+D2) = 0

is the equation of the plane through the intersection of the 2 planes. As k varies, this equation generates the family of all such planes (except the second plane itself).

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I'm really lost as to what the question has just explained. I am not grasping the concept that adding 2 planes will give you the equation of ANOTHER plane through the intersections of the first 2 planes.

As well, the question continues by asking me to find a scalar equation of the plane that passes through the ORIGIN and the line of intersection of the planes 3x+4y-7z-2=0 and 2x+3y-4=0.

Thank you to anyone who can help! God bless!