3D & Vector Basics
The Dot Product
The Cross Product
Equations of Lines & Planes
Cylinders & Quadric Surfaces
Miscellaneous
100
This is the answer to (a).
What is (x+1)^2+(y-2)^2+(z-1)^2=69 ?
100
This is the dot product of u and v.
What is 3\sqrt{2} ?
100
This is the magnitude & direction of the cross product of u and v.
What are 3\sqrt{2} and 'out of the paper/smartboard/projection surface'?
100
These are parametric equations for this line.
What are x=1+3t, y=1-2t, z=5-3t ?
100
This is an adequate description of the surface given by y=z^2 .
What is a parabolic cylinder whose generating curve is in the yz-plane and whose rulings are parallel to the x-axis?
100
This is the measure of the angle, accurate to three decimal places.
What is 70.529 degrees?
200
This is the answer to (b).
What is (y-2)^2+(z-1)^2=68 ?
200
This is the answer to (c).
What is -1?
200
This is the answer to (d).
What is -3\hat{i}-7\hat{j}-5\hat{k} ?
200
These are the parametric equations for this line.
What are x=-2+2t, y=2-t, z=4+5t ?
200
These are the intercepts of the plane given by 4x-y+2z=4 .
What are (1,0,0), (0,-4,0), and (0,0,2)?
200
This Bogus Basin lift, serving primarily beginner terrain, was named for Bill "Coach" Everts.
What is the Coach Lift?
300
This is the answer to (c).
What are (4,-1,-3) and 5?
300
This is the answer to (i)
What is -\frac{\sqrt{6}}{6} ?
300
These are the two vectors.
What are \+-\frac{1}{3\sqrt{6}}<7,2,-1> ?
300
This is the equation of this plane.
What is (x-2)+4(y-1)-3(z-0)=0 or x+4y-3z=6 ?
300
These are the traces in the coordinate planes for the surface given by -4x^2+y^2-4z^2=4 and the type of surface.
What are y^2/4-z^2=1 (yz-trace), y^2/4-x^2=1 (xy-trace), and there is no xz-trace because it's a hyperboloid of two sheets?
300
This is the magnitude of the forces in each rope.
What are 166.439 and 113.851 Newtons?
400
This is the answer to (a).
What is 11\hat{i}-4\hat{j}-\hat{k} ?
400
This is the answer to (j)
What is <-\frac{1}{6},-\frac{1}{6},\frac{1}{3}> ?
400
This is the volume of the parallelepiped.
What is 6 cubic units?
400
This is the distance.
What is \frac{3}{\sqrt{2}} ?
400
This is the z=1 trace of the surface given by 4x^2+4y^2-8y+z^2=0 , as well as a thorough description of what it actually is.
What is the circle given by x^2+(y-1)^2=3/4 , which is a circle parallel to the xy-plane, centered at (0,1,1) with a radius of \sqrt{3}/2 ?
400
The world's first lift opened in Sun Valley, Idaho in 1936, and was inspired by systems for loading this tropical fruit onto ships.
What are bananas?
500
This is the answer to (b).
What is \sqrt{14} ?
500
These are all value(s) of x.
What are x=-2,-4 ?
500
This the answer to (b).
What is \sqrt{41}/2 square units?
500
This is the distance between these two planes.
What is \frac{22}{\sqrt{26}} ?
500
This is the equation of the ellipsoid.
What is 4x^2+y^2+z^2=16 ?
500
This is a compliment that you just gave to someone else in this class.
What is the thing you just said?