# Vectors, Planes and Partial Derivatives

1.

Let a = 2i + 3j and b = -9i + 6j. Find c = a - b.

A) c = -3j

B) c = 9i

C) c = 11i + 9j

D) c = 11i - 3j

2.

Let a = 2i + 3j and b = -9i + 6j. Find d = a ? b.

A) 36

B) -36

C) 0

D) -18i2 + 18j2

3.

Find the intersection of L1: x - 2 = ½(y + 1) = 1/3(z - 3), L2: 1/3(x - 5) = ½(y - 1) = z - 4, if they intersect.

A) (-1, 2, -3)

B) (0, 0, 3)

C) (2, -1, 3)

D) They do not intersect

4.

What can we say about the plane with n = (7, 11, 0)?

A) It's perpendicular to the x-y plane

B) It's the x-y plane

C) It's parallel to the x-y plane, but offset by units along the z-axis

D) It's parallel to the x-y plane, but offset by units along the z-axis

5.

What can we say about L: x = 7 - 4t, y = 3 + 6t, z = 9 + 5t and P: 4x + y + 2z = 17?

A) They are orthogonal

B) L is co-planer with P

C) L and P are parallel

D) L intersects P at a angle relative to the z-axis

6.

Convert the following into spherical coordinates: x2 + y2 + z2 = 36

A) radians

B) (6, 0.6, )

C) = 6

D) None of the above

7.

What is the angle between these two planes: x + 2y - z = 13 & -2x - 4y + 2z = -13?

A)

B)

C)

D)

8.

A)

B)

C)

D) There is no way to know without knowing f(x,y) first

9.

A) r

B)

C)

D)

10.

A) 384 t 7

B) 8 t 8

C) 1024 t 7

D) 64 t 5

11.

A) (x + z) exp(yz + xz + xy)

B) (x + z) exp(-yz - xz - xy)

C) (x + z) exp[y(x + z)]

D) exp(yz + xz + xy)

12.

A) 0

B) Cannot be differentiated

C) 108w2

D) None of the above

13.

There are two extrema for z = 2x - x2 + 2y2 - y4. One is located at (1, 1, 2). Where is the second one located?

A) (-1, 1, 2)

B) (1, -1, 2)

C) (1, 2, -1)

D) There is no second extreme point

14.

A) Q defines a minimum

B) Q defines a maximum

C) Q defines a minimum or a maximum

D) None of the above

15.

denotes:

A) The full derivative of f

B) For all f

C) A partial derivative of f with respect to some variable

D) The gradient vector of f

16.

A)

B)

C)

D)