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Magnitude - Vector
The magnitude, or length, of the vector v→ = (a1, a2, a3) is given by,
||v→|| = √(a12 + a22 + a23)
Example of Magnitude
Illustration: Determine or find out the magnitude of each of the following vectors.
(a) a→ = (3, -5, 10)
(b) u→= (1/5, - 2/5)
(c) W→ = (0,0)
(d) i→ = (1,0,0)
Solution
There is not very much to these other than plug into the formula.
(a) ||a→|| = √(9+25+100) = √134
(b) ||u→|| = √(1/5 + 4/5) = √1 = 1
(c) ||w→|| = √(0+0) = 0
(d) ||i→|| = √(1+0+0) = 1
Properties of Vector Arithmetic If v, w and u are vectors (each with the same number of components) and a and b are two numbers then we have then following properties. v →
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