Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200...

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Page 1: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Jeopardy 203

Page 2: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Formulas 100

Lines 100

Planes 100

Surfaces 100

Curves 100

Formulas 101

Lines 200

Planes 200

Surfaces 200

Curves 200

Formulas 102

Lines 300

Planes 300

Surfaces 300

Curves 300

Formulas 103

Lines 400

Curves 400

Curves 500

Curves 600

Page 3: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

The angle between vectors u and v.

Page 4: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Arccos(u·v/|u||v|)

Page 5: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

|u x v|=

Page 6: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

|u||v|sin(θ),where θ

is the angle between the vectors

Page 7: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Volume of parallelopiped determined by vectors u, v, and w.

Page 8: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

|u·(v x w)|

Page 9: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Distance from point (x1, y1, z1) to the plane ax+by+cz+d=0

.

Page 10: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

|ax1+by1+cz1+d| / √(a²+b²+c²)

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Symmetric form of line that goes through points (3,5,7) and (1,8,4)

Page 12: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Any of the following:

1 8 4

2 3 3

x y z

3 5 7

2 3 3

x y z

1 8 4

2 3 3

x y z

Page 13: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Equation of line, in parametric form, that goes through point (3,2,1) and is normal to the plane 3x+2z=4y-5

Page 14: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

x=3+3t, y=2-4t, z=1+2t

Page 15: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

From t=1 to t=3, a particle is moving along the curve

r(t)=<3t^2, 6/t, 5>. At t=3, its velocity becomes constant. What is its position at t=6?

Page 16: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

The particle’s position will be: (81,0,5)

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What is the line of intersection of the planes 3x+2y+6z = 11 and 4x-2y-3z = 3?

Answer in parametric form.

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X=2+6t, y=5/2+33t, z = -14t

Page 19: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Find the equation of the plane that goes through the points (6,4,2), (9,7,5), and (11,16,11).

Answer in most reduced form.

Page 20: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

3x+4y-7z=20

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Find the equation of the plane that contains the lines

Answer in standard form

5 4 4

3 3 3

x y z

5 4 4

5 3 6

x y z

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9x+y-8z=81

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What are the equations of the planes that are parallel to and 3 units away from

4x-4y+2z=9?

Page 24: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

4x-4y+2z=-94x-4y+2z=27

Page 25: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Find the domain of the function

f(x,y)=ln(x²-y²)

Page 26: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

The right and left quadrants of the plane.

I.e. the right and left regions determined by the lines y=

±x

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Describe (name the type) of the x=k, y=k, and z=k traces of

-x²/25 +y²/36 – z²/4 = 100

And name the type of this surface

Page 28: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

X=k traces are hyperbolas centered on y-axis

Y=k traces are ellipsesZ=k traces are hyperbolas centered

on y-axis

The surface is a hyperboloid of two sheets

Page 29: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Give the equation, in standard form, of the surface whose projection to the x-y plane are the lines y=

±3x/2, and whose projection to the x-z plane is z=9x². What is the name of this surface?

Page 30: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

z/36 = x²/4-y²/9

Hyperbolic paraboloid

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Give the vector equation of the standard spiral (centered on the z-axis) and with radius 1.

Page 32: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

r(t)=<cos t, sin t, t>

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What is the unit tangent vector to the curve r(t)=<t^2,t-t^2, t^2+3t-2>

at t=2?

Page 34: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

1/√(74) <4,-3,7>

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Write an integral for the length of the curve <t²,2t-1,cosπ t>

From (0,-1,1) to (4,3,1)

(no need to evaluate the integral)

Page 36: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

2 2 2 2

04 4 sint t dt

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Find the length of the curve

from x=1 to x=4.

2 ln( )

2 4

x xf x

Page 38: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

7.5 +1/4 ln(4)

Page 39: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

Find the curvature of the ellipse <3cos t, sin t> at (3,0)

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3

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Find the normal vector N(t) for the curve

<4cos t, 4 sin t, t²>

at t=0.

Page 42: Jeopardy 203. Formulas 100 Lines 100 Planes 100 Surfaces 100 Curves 100 Formulas 101 Lines 200 Planes 200 Surfaces 200 Curves 200 Formulas 102 Lines 300.

N(0) = 2/√5 <-1,0,1/2>