VectorsP1^
8
4 Write, in component form, the vectors represented by the line segments
joining the following points.
(i) (2, 3) to (4, 1) (ii) (4, 0) to (6, 0)
(iii) (0, 0) to (0, −4) (iv) (0, −4) to (0, 0)
(v) (0, 0, 0) to (0, 0, 5) (vi) (0, 0, 0) to (−1, −2, 3)
(vii) (−1, − 2 , 3) to (0, 0, 0) (viii) (0, 2, 0) to (4, 0, 4)
(ix) (1, 2, 3) to (3, 2, 1) (x) (4, −5, 0) to (−4, 5, 1)
5 The points A, B and C have co-ordinates (2, 3), (0, 4) and (−2, 1).
(i) Write down the position vectors of A and C.
(ii) Write down the vectors of the line segments joining AB and CB.
(iii) What do your answers to parts (i) and (ii) tell you about
(a) AB and OC
(b) CB and OA?
(iv) Describe the quadrilateral OABC.Vector calculations
Vector calculations
multiplying a vector by a scalar
When a vector is multiplied by a number (a scalar) its length is altered but its
direction remains the same.
The vector 2 a in figure 8.11 is twice as long as the vector a but in the same
direction.When the vector is in component form, each component is multiplied by the
number. For example:
2 × (3i − 5 j + k) = 6 i − 10 j + 2 k2 ×
3
5
1
6
10
2
––
=
.
The negative of a vector
In figure 8.12 the vector −a has the same length as the vector a but the opposite
direction.a 2 aFigure 8.11