In a production of the nutcracker, at one point the sugar plum fairy holds aloft her magic wand. A splotlight whose rays are parallel to the vector [5, 3, -2] shines on the tip of this wand (which being mathematicians we will think of as a singer point) and its shadow on the stage floor lies 12 feet from the frotn of the stage. Given that the wand is being held exactly at the front of the stage, how high is the tip from the stage floor? Note that 12 feet is the distance to the front of the stage as measured along a perpendicular. It is not the distance to the position of the wand.
This is not doable without some information as to what "[5, 3 -2]" means! That is, what the coordinates mean with respect to the stage. I am going to assume that the first component is measures parallel to the front of the stage, the second component perpendicular to the from of the stage and the third component is vertical. Since the 12 feet is measured perpendicular to the stage front, we can ignore the '5'. 3 divides into 12 4 times so the actual path of the light, from the tip of the want to the tip of the shadow is 4 times the vector [5, 3, -2] itself and so the distance down it traveled was 4(-2)= -8. The tip of the wand must have been 8 feet above the stage.
Originally Posted by pyrosilver