Can somone help me with vectors?

[Kolika28]

Homework Statement

A tent with no bottom stands in a terrain. The tent has three rods that are gathered in T = (1,1,4). The tent bars stands in the points A = (0,0,0), B = (3,1,1) and C = (- 1,3,2). The tent must be supported by an additional rod which is in a point D and attached to T. The rod is perpendicular to the ground.
a) Find the length of this rod.
b) Find the coordinates of point D.

Homework Equations

The Attempt at a Solution

I do not know where to start. I thought about using DT*DC=0, but it didn't lead me anywhere. I'm struggeling with both of the tasks by the way.

 

[jedishrfu]

Read over your problem carefully there's a clue about the rod connected to D being perpendicular and connected to T.

What does that tell you about D relative to T coordinate wise? and about the length of the DT rod?

Remember don't flail about looking for some equation, try drawing a picture or make a little stick figure with straws to see what is described first.

 

[Kolika28]

Read over your problem carefully there's a clue about the rod connected to D being perpendicular and connected to T.

What does that tell you about D relative to T coordinate wise? and about the length of the DT rod?

Remember don't flail about looking for some equation, try drawing a picture or make a little stick figure with straws to see what is described first.

I have read the problem several times, and I tried to draw it both by hand and on the computer. I know it's probably easy, but I still struggle with "seeing" the new rod. At first I thought point D would share some coordinates with T, because it stood perpendicular to the ground, and therefor the height must be 4. But this is not correct. I'm sorry if I waste your time. I really try and want to understand this task.

 

[ehild]

I have read the problem several times, and I tried to draw it both by hand and on the computer. I know it's probably easy, but I still struggle with "seeing" the new rod. At first I thought point D would share some coordinates with T, because it stood perpendicular to the ground, and therefor the height must be 4. But this is not correct. I'm sorry if I waste your time. I really try and want to understand this task.

The ground is not horizontal, (green in the picture) and the pole is not vertical. But you have vectors of the ground, so you can write up the normal of the ground plane, and the equation of that plane. Knowing the normal vector of the ground, you can construct the normal line through T, and its intersection with the ground plane, and also the length of the pole.