Exam 12: Vectors and Matrices

A snow cone stand sells three sizes of snow cones: small, medium, and large. Let $\vec{N}=(56,140,83)$ give the number of each type of cone sold in one day. Let $\vec{P}=(1.50,2.00,2.50)$ give the price (in dollars) charged for each size of snow cone, $\vec{C}=(0.30,0.40,0.50)$ give the cost (also in dollars) of making each size of snow cone, and $M=(150,200,200)$ give the maximum number of each size that can be sold (because of the number of each size cup on hand.) What is the total number of cups left in the stand at the end of the day?

Jack and Jill begin walking away from a water well. Jill walks 3 meters north, and then 14 meters northeast. When Jill stops, Jack is half as far from the well as she is. How far is Jack from the well? Round numbers to 3 decimal places if necessary.

Let $P=(2,3)$ and $Q=(-3,-1)$ . Write the displacement vector $\overrightarrow{Q P}$ in component form.

The vectors $\vec{u}=8 \vec{i}-9 \vec{j}+4 \vec{k}$ and $\vec{v}=-16 \vec{i}+18 \vec{j}+8 \vec{k}$ are parallel.