Statement 1 - If A x , A y , A z are the projections of an area A on the yz , z x , x y planes respectively, then A x 2 + A y 2 + A z 2 = A 2 . Statement 2 - If l , m , n are the direction

Question

Statement 1 - If A x ​ , A y ​ , A z ​ are the projections of an area A on the yz , z x , x y planes respectively, then A x 2 ​ + A y 2 ​ + A z 2 ​ = A 2 . Statement 2 - If l , m , n are the direction cosines of the normal to the area A , then A x ​ = l A , A y ​ = m A and A z ​ = n A .

TestHub · Accepted Answer

The projection of an area on a plane is A times the cosine of the angle between the planes, so A x ​ = l A , A y ​ = m A , A z ​ = n A . Then A x 2 ​ + A y 2 ​ + A z 2 ​ = A 2 ( l 2 + m 2 + n 2 ) = A 2 . Statement 2 explains Statement 1.

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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