3D math help P(2,3,5) find the diagonal ?

Question

This is home work but not for turn in. My professor assigns it but does not pick it up.

The question.

What are the projections of the point(3,2,5) on the xy-, yz-, and xz-? Draw a rectangular box with the origin and (2,3,5) as opposite vertices and and with its faces parallel to the coordinate planes. Label all vertices of the box. Find the length of the diagonal of the box.

I believe I have this right but I want to be certain

xy = (2,3,0)

yz = (0,3,5)

xz = (2,0,5)

And the distance, or the length of the diagonal, between the origin and the projected point is √(38)

Answer 1

All your answers are correct.

Good job

Answer 2

projections of point P(3,2,5) on the coordinate planes :

the figure  I added will help you

http://i260.photobucket.com/albums/ii11/...

on xy plane it is  OP cosα where α is the angle which line OP makes with xy plane . O is origin

sinα = 5/OP

cosα = √(1 - sin²α) =  [√(OP²  -  5²)]/OP

OP cosα = √(OP²  -  5²)  =  ÃƒÂ¢Ã‚ˆÂš13

similarly projection of point P on yz plane is OPcosβ , β being the angle which OP makes with yz plane.

OP cosβ = √(OP²  -  3²)  =  ÃƒÂ¢Ã‚ˆÂš29

and projection on xz plane = √(OP²  -  2²) =  ÃƒÂ¢Ã‚ˆÂš34

length of the diagonal, between the origin and the projected point is √(38) which is the distance of the point (2,3,5) from origin.

the vertices you labelled on coordinate planes are right .

xy = (2,3,0)

yz = (0,3,5)

xz = (2,0,5)

other vertices are

origin(0,0,0)

(2,0,0)

(0,3,0)

(0,0,5)