Chapter 4: Vector operations

Fill in the Blank:

 

1.             A ____________ is a magnitude without direction.

2.             ____________ is the vector version of distance.

3.             The two different forms of coordinates for describing a vector in 2D are ____________ .

4.             You cannot add vectors in ____________ unless they are in the same direction.

5.             Scalar multiplication affects a vector’s ____________ .

6.             To normalize a vector in polar coordinates, change the magnitude to 1 and leave the ____________ the same.

7.             For vectors C=[3 6] and D=[8 -4], are C and D perpendicular?

8.             The cross product of two vectors is known as the ____________.

9.             A cross product produces a third vector which is ____________ to the original two.

Matching:

 

10.         An object on a screen has an initial position of (400,625). Match its final position with the corresponding displacement:

            I.    (400,800)                A. -200

            II.   (200,625)                B. -400

            III. (400,825)                C. 225

            IV. (625,625)                D. 175

            V.  (400,225)                E. 200

11.         Match the polar coordinate to its corresponding Cartesian coordinate:

            I.    B=4î +3ĵ                  A. 5.83 units @ 31º

            II.   B=2î +4ĵ                  B. 6.71 units @ 26.6º

            III. B=5î +3ĵ                  C. 4.47 units @ 63.4º

            IV. B=6î +3ĵ                  D. 1.41 units @ 45º

            V.  B=î +ĵ                     E. 5 units @ 36.9º

12.         Given:

A = 2î + 3ĵ + 6

B = 7î + 2ĵ

C = 14ft@80º

D = 5î – ĵ + 2

E = 3î + 11ĵ

Match the following vector equations with their corresponding sum:

            I.    A - D                     A. -4î + 9ĵ

            II.   B + C                     B. -3î + 4ĵ + 4

            III. E - B                      C. 10î + 13ĵ

            IV. C + E                     D. 9.43î + 15.79ĵ

            V.  B + E                     E. 5.43î + 24.79ĵ

13.         Match each vector A with the result 3A:

            I.    A = 4î + ĵ +-3       A. 3A = 21î – 14ĵ

            II.   A = 3ft @ 75º         B. 3A = 27ft @ 25º

            III. A = 2î + 7ĵ              C. 3A = 9ft @ 75º

            IV. A = 9ft @ 25º         D. 3A = 12î +3ĵ -9

            V.  A = 7î - 8ĵ               E. 3A = 6î + 21ĵ

14.         Match each vector with its normalized form:

            I.    A = 5ft @ 60º         A. Â =

            II.   A = [3 4]                B. Â = 1ft @ 40º

            III. A = [5 12]               C. Â = 1ft @ 60º

            IV. A = 20ft @ 40º        D. Â =

            V.  A = [1 2 2]              E. Â =

15.         Given:  vectors A = [a1 a2], B = [b1 b2], and θ = the angle between two vectors. Match the left and right sides of the vector statements:

            I.    If C●D = 0,             A. then θ > 90°.

            II.   If A●B < 0,             B. then θ < 90°.

            III. If A●B > 0             C. then AB.

16.         Given: A=[-2 1 6]   B=[3 5]   C=[-1 1]   D=[3 -2 6]   E=[3 7 -4] F=[4 6].  Match the dot product to its equivalent scalar product:

            I.    -23                         A. E●D

            II.   -44                         B. C●B

            III. 19                           C. A●E

            IV. 2                            D. F●B

            V.  42                           E. A●D

17.         Find the cross product AB for each set of vectors:

            I.    [-14 -34 -6]             A. A = [2 1 5] and B = [3 2 3]

            II.   [7 -9 1]                   B. A = [4-2 2] and B = [-5 1 6]

            III. [-7 9 1]                   C. A = [8 1 0] and B = [2 -1 3]

            IV. [3 -24 -10]              D. A = [3 2 3] and B = [2 1 5]

18.         Given  for vectors A and B. Match the given information with the corresponding angle between vectors A and B.

            I.    θ = 40.12                A.

            II.   θ = 14.71                B.

            III. θ = 42.71                C.

            IV. θ = 44.17                D.

            V.  θ = 54.98                E.

19.         Match each cross product to its corresponding surface normal:

            I.    [2 10 12]  A. [-0.424  -0.566  0.707]

            II.   [-5 0 7]    B. [0.874  0.389  -0.291]

            III. [9 4 -3]    C. [-0.546  0  0.764]

            IV. [6 7 2]     D. [0.636   0.742   0.212]

            V.  [-3 -4 5]   E. [0.127  0.635  0.762]