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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. 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.

2. 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.

3. Given a vector a = 6i - 8j. Calculate the unit vector in the direction of a.

  1. (35)i - (45)j
  2. (610)i + (810)j
  3. -(35)i + (45)j
  4. (45)i - (35)j
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Answer: A

|a| = √62 + (-8)2 = √36 + 64 = √100 = 10. The unit vector = a / |a| = 6i - 8j10 = (35)i - (45)j.

4. 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.

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. Given two non-zero vectors u and v such that u = (k - 3)v. If u and v are parallel, which statement regarding k is correct?

  1. k can be any real number except 3
  2. k must be greater than 0
  3. k must equal 0
  4. k = 3
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Answer: A

For non-zero vectors to be parallel, u = m*v where scalar m ≠ 0. Here m = k - 3, so k - 3 ≠ 0, which means k can be any real number except 3.

7. 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.

8. 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.

9. Given vector a = 4i - 3j and vector b = h i + 4j. If |a| = |b|, find the positive value of h.

  1. 3
  2. 4
  3. 5
  4. 1
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Answer: A

|a| = √42 + (-3)2 = √25 = 5. |b| = √h2 + 42 = √h2 + 16. Setting |a| = |b| gives 5 = √h2 + 16 => 25 = h2 + 16 => h2 = 9 => h = 3.

10. The position vectors of points A and B relative to origin O are ~a = 2i + 7j and ~b = 5i - 2j respectively. Express AB in column vector form.

  1. (-3, 9)^T
  2. (7, 5)^T
  3. (3, -9)^T
  4. (-7, -5)^T
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Answer: C

AB = OB - OA = (5i - 2j) - (2i + 7j) = (5-2)i + (-2-7)j = 3i - 9j, which in column vector form is (3, -9)^T.

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