Question:
prove that2x+3y+7=0represents a plane perpendicular to xy-plane.
Answer:
Given, equation of the plane is 2x + 5y + 7 = 0
Now, direction ratios of normal to the plane are 2, 5, 0
Equation of xy-plane is z = 0
direction ratios of normal to the plane are 0, 0, 1
Now, a1 * a2 + a1 * a2 + a1 * a2
= 2 * 0 + 5 * 0 + 0 * 7
= 0 + 0 + 0
= 0
So, 2x + 5y + 7= 0 represents a plane perpendicular to xy-plane.
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