arrow_backBack to Study Resources

Quiz Chapter 8: Vectors

10 questions · Form 4 Additional Mathematics Bab 8: Vectors

Question 1 of 10Score: 0

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

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 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
Show answer

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.

2. Given 3a - 2b = c. If a = 2i + j and c = 4i - 5j, find vector b.

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

Answer: A

3a - c = 2b => 2b = 3(2i + j) - (4i - 5j) = (6i + 3j) - (4i - 5j) = 2i + 8j. Dividing by 2 gives b = i + 4j.

3. 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
Show answer

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.

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
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.

5. Which of the following is a scalar quantity?

  1. Velocity
  2. Displacement
  3. Electric Current
  4. Acceleration
Show answer

Answer: C

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

6. 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).

7. 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
Show answer

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.

8. 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
Show answer

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.

9. Points P, Q, and R are collinear. Given PQ = 2i + 5j and PR = 6i + kj, find the value of k.

  1. 10
  2. 12
  3. 15
  4. 18
Show answer

Answer: C

Since P, Q, and R are collinear, PR = m*PQ. Comparing i-components: 6 = m(2) => m = 3. Comparing j-components: k = m(5) = 3(5) = 15.

10. 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.

Sponsored