Question

Three planes, E, F, and G intersect so that each is perpendicular to the other two. A segment AB is positioned so that the length of its projection on the intersection of E and F is 1, on the intersection of F and G is 2, and on the intersection of E and G is 3. What is the length of AB?

A) radical 14
B) 4
C) 5
D) 6
E) radical 12

Answer 1

Three planes, E,F and G, intersect so that each is perpendicular to the other two. A segment AB is positioned so that the
Length of its projection on the intersection of E and F = 1,
Length of its projection on the intersection of F and G = 2
Length of its projection on the intersection of E and G = 3.
Length of AB =√{(1)²+(2)²+(3)²}=√{1+4+9}=√14
Hence a.