Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Which of the following is not a vector quantity?
A | mass | B | acceleration | C | displacement | D | velocity | E | force |
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2.
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An orienteer runs 4 km at a bearing of 60° and then 3 km at a bearing of
150°. Find her distance and bearing from the starting point.
A | 5 km at a bearing of 97° | B | 5 km at a bearing of
83° | C | 5.7 km at a bearing of 97° | D | 6.5 km at a bearing of
83° | E | 5.7 km at a bearing of 102° |
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3.
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If A is (–2, 1) and B is (3, 2), sketch the vector AB on the
Cartesian plane.
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4.
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Calculate the norm of the position vector of
P(–8, 6).
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5.
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Calculate to the nearest degree the angle the vector  makes with the
positive x-axis.
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6.
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How would the vector –3a compare with the vector a?
A | It would be three times as long and in the same direction. | B | It would be three
times as long and in the opposite direction. | C | It would be the same length and direction with
angle tripled. | D | It would be three times as long in the opposite direction with the angle
tripled. | E | It would be the same length in the opposite direction with the angle
tripled. |
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7.
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Find a + b if a = (5, 170º) and b = (7,
90º).
A | (9.3, 122º) | B | (7.9, 122º) | C | (9.3,
166º) | D | (7.9, 166º) | E | (–9.3,
302º) |
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8.
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Calculate (5, 90º) – (12, 0º).
A | (13, 23º) | B | (13, 157º) | C | (13,
337º) | D | ( , 23º) | E | ( ,
337º) |
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9.
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Which of the following is the vector j?
A | (0, 0) | B | (1, 0) | C | (0,
1) | D | (–1, 0) | E | (0, –1) |
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10.
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Write the vector  as a linear combination of i and
j. A | –4i + 7j | B | (–4i,
7j) | C |  | D | (7i, 4j) | E | 7i –
4j |
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11.
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If r = (–2, 4), find an exact expression for  .
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12.
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If a = –5i – 2j and b = –3i
+ 4j find 2a – 3b.
A | –i – 16j | B | –19i +
16j | C | –8i + 2j | D | 8i – 6j | E | 3i –
2j |
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13.
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Resolve the vector (8, 300°) into i and j
components.
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14.
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Railway lines are running north-south. Two people are pulling on a trolley in
the northerly direction. The first person is pulling with a force of 900 N in a direction of 19º
east of north and the other 500 N in a direction of 12º west of north. Find the net force in the
direction of the tracks (north).
A | 1329 N | B | 1340 N | C | 1367
N | D | 1386 N | E | 1400 N |
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15.
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A car is travelling at 60 km/h at a bearing of 230°. It turns and changes
speed so it is now travelling at 85 km/h at a bearing of 200°. By how much has its velocity
changed?
A | 45 km/h at a bearing of 154° | B | 59 km/h at a bearing of
154° | C | 45 km/h at a bearing of 158° | D | 59 km/h at a bearing of
158° | E | 25 km/h at a bearing of 330° |
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16.
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A boat is heading at a bearing of 320º with a speed through the water of 12
km/h. There is a current of 6 km/h at a bearing of 190º. Find the true speed of the boat and the
course made good.
A | 9.4 km/h at a bearing of 291º | B | 16.5 km/h at a bearing of
291º | C | 9.4 km/h at a bearing of 315º | D | 16.5 km/h at a bearing of
315º | E | 18 km/h at a bearing of 255º |
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