Length of a Vector Flashcards

All 5 cards in this deck

What does the notation $|\mathbf{a}|$ mean?

The magnitude (length) of the vector $\mathbf{a}$.

What is the formula for the magnitude of the vector $\begin{pmatrix}x\\y\end{pmatrix}$?

$\sqrt{x^2+y^2}$

What are the steps to find the length of a column vector?

e.g. $\begin{pmatrix}3\\-4\end{pmatrix}$

1. Square each component: $9$ and $16$
2. Add them: $25$
3. Take the square root: $5$

True or false? $\begin{pmatrix}-3\\4\end{pmatrix}$ and $\begin{pmatrix}3\\-4\end{pmatrix}$ have the same magnitude.

True. Squaring removes the signs, so only the directions differ.

If a vector is multiplied by the scalar $k$, what happens to its length?

The length is multiplied by $|k|$.

e.g. $|3\mathbf{a}|=3|\mathbf{a}|$