IB Mathematics Analysis and Approaches Question Type 4: Finding the Magnitude of Vectors Exercises

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}-2\\ 5\end{array}\right)$ and its unit vector.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}0\\ -7\\ 24\end{array}\right)$ and its unit vector.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}2\\ -1\\ 2\end{array}\right)$ and its unit vector.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}-\sqrt{3}\\ 1\\ 2\end{array}\right)$ and its unit vector.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}-3\\ 4\\ 12\end{array}\right)$ and its unit vector.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}5\\ -5\\ 5\end{array}\right)$ and its unit vector.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}\frac{1}{2}\\ -\frac{3}{2}\end{array}\right)$ and its unit vector.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}1\\ 2\\ 2\end{array}\right)$ and the unit vector in the direction of $\mathbf{v}$.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}\sqrt{2}\\ \sqrt{2}\\ \sqrt{2}\end{array}\right)$ and a unit vector in the direction of $\mathbf{v}$.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}\frac{3}{2}\\ -\frac{3}{2}\\ 0\end{array}\right)$ and find a unit vector in the direction of $\mathbf{v}$.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}1\\ -1\\ 1\\ -1\end{array}\right)$ in ${\mathbb{R}}^4$ and its unit vector.

Find the magnitude of the vector $\mathbf{v}=\left(\begin{array}{c}3\\ 4\end{array}\right)$ and its unit vector.