In my calculus and vectors course, I have been assigned the following problem:
In an archery challenge an arrow is fired from the point (3,4,-1) and is aimed at the plane x+y+z-30=0 such that x,y,z are greater than or equal to 0. Each shot is given a score by taking the point where the arrow hit the plane and multiplying the 3 coordinates together.
a) If a player shoots the arrow along a direction of [1,1,1] determine the score for their shot (I have solved this one, the answer being (11)(12)(7)=924)
b) Determine the direction that the player should aim in order to maximize their score.
I need help with (b). any help would be greatly appreciated!