26.2 Modulus of a Vector

The modulus of a vector is its magnitude. i.e The modulus of a vector \(\overrightarrow {PQ}\) is written as \(\left |\overrightarrow {PQ}\right |\). If a vector is represented by \(\underline {a}\), then its modulus is \(\left |\underline {a}\right |\).

Two vectors are equal if and only if they are equal in length and have the same direction.

The zero vector has zero magnitude. It has no direction — there is no way to point a segment of length nothing — which is why it is the one vector for which “direction” is left undefined, and why it must be excluded whenever a direction is required.

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