Thread: Vector

How long is the shadow cast on the ground (represented by the xy-plane) by a pole that is eight meters tall, given that the Sun's rays are parallel to the vector [5,3,-2]?

This problem confuses me. Doesn't the location of the pole matter?

Originally Posted by Veronica1999

How long is the shadow cast on the ground (represented by the xy-plane) by a pole that is eight meters tall, given that the Sun's rays are parallel to the vector [5,3,-2]?

This problem confuses me. Doesn't the location of the pole matter?

let the pole be at the origin of the xy plane, represented by the vector

let the vector represent a sun ray vector from the top of the pole to the ground.

... the resulting shadow vector lying on the xy plane.

since the shadow vector lies on the ground, ...

<0,0,8> + <20,12,-8> = <20,12,0>

magnitude of the shadow vector ...

Well, there is one piece of information which is not explicitly given in that assignment: the Sun's rays are all parallel with each other (because the Sun is very far away from us). That's why it doesn't matter where on the xy-plane the pole is.

Well, if the pole is in Seattle, Wash., there will be no shadow because the sun will covered by clouds!