Vectors Practice Questions
Additional Mathematics — SPM Standard Questions
Question 1 (Exam Watch 6)
SPM Clone '07 / '10
It is given that p = i + 2j, q = 3i + 13j and r = 3i + 9j.
(a) Find p + q + r and |p + q + r|.
(b) Hence, find the unit vector in the direction of p + q + r.
Question 2 (Exam Watch 7)
SPM Clone '07
It is given that a = 7 and b = 1 .
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(a) Find b − a and |b − a|.
(b) Hence, find the unit vector in the direction of b − a.
Question 3 (Exam Watch 8)
SPM Clone '04
Given that O(0, 0), P(−2, 3) and Q(13, 8) and R is a point on PQ such that PR =
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PQ, find
in terms of unit vectors, i and j,
(a) PQ,
(b) OR.
Question 4 (Exam Watch 9)
SPM Clone '03
Given that a = 3i + 2j, b = 2i − 4j and c = i − 10j. If c = ka + tb, find the value of k and of t.
Question 5 (Exam Watch 10)
SPM Clone '06 / '12
It is given that a = 2i − 5j and b = ki − 3j. If the vectors a and b are parallel, find
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(a) the value of k,
(b) |a| : |b|.
Question 6 (Exam Watch 11)
SPM Clone '09
Given that p = 3 and q = k , find the value of k if |p − q| = 10.
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Question 7 (Example 18)
Worked Example
It is given that OA = 9i − 10j, OB = 4i + 2j and OC = ki − 2j, where O is the origin.
(a) Find the unit vector that is parallel to the vector AB.
(b) Find the value of k such that the points A, B and C are collinear.
(c) In the case where k = 1, find
(i) the value of m and of n for which OA + mOB + nOC = 0,
(ii) the vector OD such that ABCD is a parallelogram.
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