Pure · Vectors
Chapter 1 · 3
The idea
Magnitude and direction of a vector
The magnitude of a vector as Pythagoras on its components (left as an exact surd), unit vectors as a vector scaled to length one, direction as an angle or bearing, and finding the angle in a vector triangle with the cosine rule.
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Pure · Vectors
Magnitude and direction of a vector
The magnitude of a vector as Pythagoras on its components (left as an exact surd), unit vectors as a vector scaled to length one, direction as an angle or bearing, and finding the angle in a vector triangle with the cosine rule.
Why it works
Pythagoras on the components
The magnitude (or modulus) of a vector, written , is the length of its arrow. Lay the components out as the legs of a right-angled triangle and the arrow is the hypotenuse, so Pythagoras gives:Square each component, add, then square-root — and as with any length, leave it as an exact surd (, not ) unless a decimal is asked for. Because the components are squared, their signs make no difference to the size.
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The rest of the explanation, plus 4 worked examples you step through move by move.
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