10 questions · Form 4 Additional Mathematics Bab 8: Vectors
Which set of vector equations correctly illustrates the Triangle Law of Addition for points P, Q, and R?
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?
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. 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.
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).
3. Given vector a = 4i - 3j and vector b = h i + 4j. If |a| = |b|, find the positive value of h.
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. If vector OA = 3i - 4j and vector OB = -i + 2j, calculate the distance between points A and B.
Answer: A
AB = OB - OA = (-i + 2j) - (3i - 4j) = -4i + 6j. Distance = |AB| = √((-4)2 + 62 = √(16 + 36) = √52 = 2√13.
5. Which of the following is a scalar quantity?
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. Points P, Q, and R are collinear. Given PQ = 2i + 5j and PR = 6i + kj, find the value of k.
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.
7. 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.
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.
8. If vector AB = ~a + 3~b and vector CD = 4~a + 12~b, which statement correctly describes the relationship between AB and CD?
Answer: B
CD = 4~a + 12~b = 4(~a + 3~b) = 4AB. Since CD = k*AB with k = 4 (a non-zero scalar), AB is parallel to CD and CD = 4AB.
9. In a parallelogram ABCD, AB = 4i + 2j and AD = -i + 5j. Find the position vector of C if A is at the origin.
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.
10. Given OP = 4i - 3j and OQ = (k + 1)i + 9j. If OP is parallel to OQ, find the magnitude of OQ.
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.