Question

What does the equations 4x+3y-2z+5 = 0 and 3y-4x+2z+10 = 0 together represent?

• A. Straight line
• B. Point
• C. One side of two intersecting planes
• D. Intersection of two planes

Answer 1

Answer: (A), (D)

The correct options are
A Straight line
D Intersection of two planes

We want to know what the equations 4x+3y-2z+5 = 0 and 3y-4x+2z+10 = 0 together represent. This will give us the intersection of the two equations given or all the points on the curve thus obtained should satisfy both the equations. We know that equations of the form ax+by+cz+d = 0 represents a plane. The given two equations represent two planes. We saw that intersection of two non parallel planes gives a straight line. The dark directed line in the diagram represents the intersection of two planes