Одиничні вектори

Vectors are quantities that have both direction and magnitude. The magnitude is the length of a vector.

The magnitude of a vector is denoted as $\vec{u}$ = $<a,b>$ .

We measure the magnitude of vector using the following formula:

$\vec{u}$ = $\sqrt{a^2+b^2}$

You can use Pythagorean Theorem to think about the magnitude of a vector. In the diagram below:

The distance between points X and Y = $a$; the first value given in vector $|\vec{u}|$.

The distance between points Y and Z = $b$; the second value given in vector $|\vec{u}|$.

The distance between points Z and X = $\sqrt{a^2+b^2}$

By plugging the values given in the vector $|\vec{u}|$ into the Pythagorean function $a^2+b^2 = c^2$, the value $\sqrt{c^2}$, the magnitude of the vector, is returned.

Now that we have discussed magnitude, we must learn the importance of the direction which a vector goes in.

Take, for example, an airplane pointing north. If a strong wind is blowing from the north-west, the plane will fly more north-east.

A unit vector is a vector with a magnitude of 1 that points in the same direction as another vector. To find the unit vector you multiply the vector by $\frac{1}{magnitude}$