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Magnitude of a Vector

Magnitude of a Vector

A column vector gives both magnitude and direction. The magnitude, or size, of a vector is written as |a| (called modular a, when the sign is ignored). When considering just the size (magnitude) of the vector, the direction is irrelevant.

Because a column vector uses rectangular components (ie at right angles) the magnitude of the vector can be obtained using Pythagoras: for a vector `((x),(y))`, this is `sqrt(x^2 + y^2)`.

Magnitude of a vector

Example 1

What is the magnitude of the resultant vector `3bb(g) + 2bb(h)`, when `bbg = ((2),(5))` and `bb(h) = ((1),(-1))`?

Give your answer to 2 decimal places.

The resultant vector is `((3 xx 2 + 2 xx 1),(3 xx 5 + 2 xx -1)) = ((8),(13))`

Using Pythagoras: `a^2 = b2 + c^2`

= `sqrt(8^2 + 13^2)`

= 15.264

=15.26 (2dp)

Answer: 15.26

Example 2

Vector c is defined as `((7),(11))`.

What is the magnitude of c?

Use Pythagoras to determine the magnitude:

magnitude = `sqrt(7^2 + 11^2)`

= 13.038

Answer: 13.04 (to 2dp)

See also Pythagoras