What is the nature of the intersection of the set of planes `x+a y+(b+c)z+d=0,x+b y+(a+a)z+d=0a n dx+c y+(a+b)z+d=0?` a. they meet at a point b. the form a triangular prism c. the pass through a line d. they are at equal distance from the origin

Options

A. They meet at a point
B. They form a triangular prism
C. They pass through a line
D. They are at equal distance from the origin

Answer

c

Explanation

`|{:(1,,a,,b+c),(1,,b,,c+a),(1,,c,,a+b):}|=|{:(1,,a,,a+b+c),(1,,b,,a+ b+ c),(1,,c,,a+b+c):}|=0`