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Quiz Chapter 8: Vectors

10 questions · Form 4 Additional Mathematics Bab 8: Vectors

10 questions · plays in fullscreen

Full Question List & Answer Key

Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.

1. Given vectors p = 3i - 2j and q = -i + 4j. Find the magnitude of 2p + q.

  1. 5
  2. √29
  3. √41
  4. √37
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Answer: A

2p + q = 2(3i - 2j) + (-i + 4j) = (6i - 4j) + (-i + 4j) = 5i + 0j. Magnitude = √52 + 02 = 5.

2. Which of the following is a scalar quantity?

  1. Velocity
  2. Displacement
  3. Electric Current
  4. Acceleration
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Answer: C

Electric current is a scalar quantity as it has magnitude only. Velocity, displacement, and acceleration all possess both magnitude and specific direction.

3. In a parallelogram ABCD, AB = 4i + 2j and AD = -i + 5j. Find the position vector of C if A is at the origin.

  1. 3i + 7j
  2. 5i - 3j
  3. -5i + 3j
  4. 3i - 7j
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Answer: A

By the Parallelogram Law, AC = AB + AD. Since A is at origin O, OC = AC = (4i + 2j) + (-i + 5j) = (4 - 1)i + (2 + 5)j = 3i + 7j.

4. Which set of vector equations correctly illustrates the Triangle Law of Addition for points P, Q, and R?

  1. PR + RQ = PQ
  2. PQ + QR = PR
  3. PQ + PR = QR
  4. QR + PR = PQ
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Answer: B

According to the Triangle Law, starting at point P, moving along PQ, and then along QR gives the net displacement from initial point P to final point R, so PQ + QR = PR.

5. Vectors a and b are non-zero and non-parallel. If (h - 2)a + (k + 5)b = 0, find the values of h and k.

  1. h = 2, k = -5
  2. h = -2, k = 5
  3. h = 2, k = 5
  4. h = 0, k = 0
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Answer: A

Since a and b are non-zero and non-parallel, (h - 2)a + (k + 5)b = 0 holds if and only if both coefficients are zero: h - 2 = 0 => h = 2, and k + 5 = 0 => k = -5.

6. Vector r has a magnitude of 13 units and is in the direction of vector 5i - 12j. Express r in linear combination form.

  1. 5i - 12j
  2. 13i - 13j
  3. (513)i - (1213)j
  4. -5i + 12j
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Answer: A

Magnitude of (5i - 12j) = √52 + (-12)2 = √25 + 144 = √169 = 13 units. Since r has a magnitude of 13 units in that direction, r = 5i - 12j.

7. Given that vector r = xi + yj is a unit vector. Which equation expresses the relationship between x and y?

  1. x2 + y2 = 1
  2. x + y = 1
  3. √x + y = 1
  4. x2 - y2 = 1
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Answer: A

By definition, a unit vector has a magnitude of 1. |r| = √x2 + y2 = 1. Squaring both sides gives x2 + y2 = 1.

8. Given OP = 4i - 3j and OQ = (k + 1)i + 9j. If OP is parallel to OQ, find the magnitude of OQ.

  1. 15
  2. 20
  3. 25
  4. 18
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Answer: A

Since OP \parallel OQ, OQ = m*OP => (k+1)i + 9j = m(4i - 3j). From j-components: 9 = -3m => m = -3. Thus OQ = -3(4i - 3j) = -12i + 9j. Magnitude |OQ| = √(-12)2 + 92 = √144 + 81 = √225 = 15.

9. If vector OA = 3i - 4j and vector OB = -i + 2j, calculate the distance between points A and B.

  1. 2√13
  2. √20
  3. 2√5
  4. √10
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Answer: A

AB = OB - OA = (-i + 2j) - (3i - 4j) = -4i + 6j. Distance = |AB| = √(-4)2 + 62 = √16 + 36 = √52 = 2√13.

10. If unit vector in the direction of vector k i + 8j is (35)i + (45)j, determine the value of k.

  1. 6
  2. 10
  3. 12
  4. 15
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Answer: C

The ratio of i-component to j-component of the unit vector is (35) / (45) = 34. Therefore, k8 = 34 => 4k = 24 => k = 12.

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