Norms

Practice Questions

Linear Algebra › Norms

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1

Find the norm of the vector $\vec{v} = (4, 3, 0)$

2

$\textbf{u} = \left (\frac{3}{5} \cos \theta ,\frac{4}{5} \sin \theta , -\frac{3}{5} \sin \theta, -\frac{4}{5} \cos \theta \right )$

True or false: $\textbf{u}$ is a unit vector regardless of the value of $\theta$ .

3

Which of these functions could be that of a Euclidean norm operator? You may assume each function is onto.

4

$\textbf{u} = \left ( \cos \theta , \frac{1}{6}, \sin \theta \right )$ .

To the nearest hundredth (radian), which of the following values of $\theta$ would make $\textbf{u}$ a unit vector?

5

$\textbf{u} = \left (\cos \theta , \frac{1}{2} , \frac{2}{3} \right )$

Evaluate $\theta \in [0, 2 \pi]$ (nearest hundredth of a radian) to make $\textbf{u}$ a unit vector.

6

Find a unit vector in the same direction as $\vec{v} = (2, -3, \sqrt{3})$

7

$\textbf{u} = \left ( \frac{1}{4}, \frac{1}{3} , \ln a \right )$ .

Evaluate to make $\textbf{u}$ a unit vector.

8

Find the norm of the vector $\vec{v} = (-1, 3, 2,2)$

9

Find the norm, $\begin{Vmatrix} \bf{a} \end{Vmatrix}$ , given $\bf{a}= \begin{bmatrix} 2\ 1\ 7\ -2 \end{bmatrix}$

10

Find the norm of vector .

$A=(\cos(x), \sin(x))$

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