arrow_backBack to Study Resources

Quiz Chapter 8: Vectors

10 questions · Form 4 Additional Mathematics Bab 8: Vectors

Question 1 of 10Score: 0

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

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 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
Show answer

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.

2. 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
Show answer

Answer: A

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

3. 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
Show answer

Answer: A

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

4. 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
Show answer

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.

5. Vector a has magnitude 10 units making an angle with the positive x-axis such that cos θ = 0.6 and sin θ = 0.8 in the first quadrant. Express vector a in Cartesian component form.

  1. 6i + 8j
  2. 8i + 6j
  3. 0.6i + 0.8j
  4. 6i - 8j
Show answer

Answer: A

Vector a = |a|cosθ i + |a|sinθ j = 10(0.6)i + 10(0.8)j = 6i + 8j.

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

  1. 5
  2. √29
  3. √41
  4. √37
Show answer

Answer: A

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

7. 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
Show answer

Answer: A

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

8. Given that vector u = (p + 2)i + 12j is parallel to vector v = 3i + 4j. Determine the value of p.

  1. 7
  2. 9
  3. 5
  4. 11
Show answer

Answer: A

Since u \parallel v, u = k*v => (p + 2)i + 12j = k(3i + 4j). From j-components: 12 = 4k => k = 3. From i-components: p + 2 = 3k = 3(3) = 9 => p = 7.

9. In a triangle ABC, vector AB = u and vector AC = v. M is the midpoint of BC. Express vector AM in terms of u and v.

  1. 12 (u + v)
  2. u + 12 v
  3. 12 (u - v)
  4. v - 12 u
Show answer

Answer: A

BC = AC - AB = v - u. BM = 12 BC = 12 (v - u). AM = AB + BM = u + 12(v - u) = 12 u + 12 v = 12 (u + v).

10. 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
Show answer

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.

Sponsored