Question Type 4: Finding the magnitude of vectors Exercises

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} -2 \\ 5 \end{pmatrix}$ and its unit vector.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} 0 \\ -7 \\ 24 \end{pmatrix}$ and its unit vector.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} 2 \\ -1 \\ 2 \end{pmatrix}$ and its unit vector.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} -\sqrt{3} \\ 1 \\ 2 \end{pmatrix}$ and its unit vector.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} -3 \\ 4 \\ 12 \end{pmatrix}$ and its unit vector.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} 5 \\ -5 \\ 5 \end{pmatrix}$ and its unit vector.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} \frac{1}{2} \\ -\frac{3}{2} \end{pmatrix}$ and its unit vector.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} 1 \\ 2 \\ 2 \end{pmatrix}$ and the unit vector in the direction of $\mathbf{v}$.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} \sqrt{2} \\ \sqrt{2} \\ \sqrt{2} \end{pmatrix}$ and a unit vector in the direction of $\mathbf{v}$.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} \frac{3}{2} \\ -\frac{3}{2} \\ 0 \end{pmatrix}$ and find a unit vector in the direction of $\mathbf{v}$.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} 1 \\ -1 \\ 1 \\ -1 \end{pmatrix}$ in $\mathbb{R}^4$ and its unit vector.

Find the magnitude of the vector $\mathbf{v} = \begin{pmatrix} 3 \\ 4 \end{pmatrix}$ and its unit vector.