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1. If Write each of the following as column vectors. |
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a
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3a
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b
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a + b
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c
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2a + 3b
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d
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b − a
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e
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c − a − b
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f
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a + (b − c)
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g
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2(a + b)
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h
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-6b
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2. If 
(i) Write a, b and c in terms of unit vectors.
(ii) Use unit vectors to calculate
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a
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2a
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b
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b + c
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c
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4c + 2b
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d
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a − b
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e
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b − a + c
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f
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b − (a + c)
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g
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3(b + c)
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h
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-3c
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3. If r = 3i − 2j + 4k, s = 3i + 2j and t = 2i − 3j + 4k find 3r + 2s - t
Give the answer as a column vector.
4. A and B are points with coordinates (3, 2, 1) and (5, 3, -2) respectively. Find the vector AB as both a column vector and in terms of unit vectors.
5. For the following set of points determine whether the point R lies on the line PQ.
P = (-3, 1, 3) , Q = (3, 1, 0) and R = (5, 1, -1)
6. Four points P, Q, R and S have position vectors 3i - j + 7k, 4i + k, i - j + k and -2j + 7krespectively. Find the displacement vectors PQ and SR. What can you say about the quadrilateral PQRS?
