J13
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1 1 4 2<br />
(b) b = = <br />
2 2 10<br />
5<br />
2<br />
1 4 6 2<br />
(c) 3a - 21<br />
b = 3<br />
= + <br />
3<br />
2 10<br />
9<br />
5<br />
8 <br />
= .<br />
4<br />
2 4<br />
(d) 3a + 2b = 3 + 2 <br />
3<br />
10<br />
6 8 2 <br />
= + = <br />
9<br />
20 29 <br />
Note: When a vector is multiplied by a positive scalar, its direction does not change.<br />
However, when a vector is multiplied by a negative scalar, its direction is reversed.<br />
The magnitude of a vector<br />
The length of a vector is called magnitude. In the figure below the magnitude of OA is<br />
the length of line OA and is denoted as OA or a or a.<br />
Triangle OAB is right-angled at point B. We can use the Pythagoras’ theorem to find the<br />
length of line OA. Thus<br />
2<br />
OA OB BA<br />
= 6 2 + 3 2<br />
= 36 + 9<br />
= 45<br />
OA = 45<br />
Therefore, OA = a = 6.708 units.<br />
Note that the column vector of OA is<br />
2<br />
2<br />
6<br />
and OA is<br />
2 2<br />
6 3 .<br />
3
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