IB Mathematics Applications & Interpretation Question Type 2: Finding the Angle Between Two Different Vectors Exercises

Given two vectors $\mathbf{a}$ and $\mathbf{b}$ satisfy $\mathbf{a}\cdot \mathbf{b}=5$, $|\mathbf{a}|=3$, and $|\mathbf{b}|=4$, find the angle $\theta$ between $\mathbf{a}$ and $\mathbf{b}$.

Find the value of $t$ such that the angle between the vectors $\left(\begin{array}{c}1\\ 0\\ t\end{array}\right)$ and $\left(\begin{array}{c}0\\ 1\\ 1\end{array}\right)$ is $60^{\circ }$.

Find the angle between $\overrightarrow{OA}$ and $\overrightarrow{OB}$, where $A=(2,0,1)$ and $B=(1,2,2)$.

Find the angle between the vectors $\left(\begin{array}{c}4\\ 1\\ -4\end{array}\right)$ and $\left(\begin{array}{c}1\\ -2\\ 2\end{array}\right)$.

Let $\mathbf{a}$ and $\mathbf{b}$ be vectors such that $|\mathbf{a}|=4$, $|\mathbf{b}|=3$ and $\mathbf{a}\cdot \mathbf{b}=6$.

Find the angle between the vectors $\mathbf{a}+\mathbf{b}$ and $\mathbf{a}-\mathbf{b}$.

Calculate the angle between the vectors $\left(\begin{array}{c}2\\ -1\\ 2\end{array}\right)$ and $\left(\begin{array}{c}1\\ 2\\ 3\end{array}\right)$.

Calculate the angle between the vectors $\mathbf{a}=\left(\begin{array}{c}1\\ 4\\ 3\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}2\\ 1\\ 2\end{array}\right)$.

Determine the angle between the vectors $\left(\begin{array}{c}1\\ 1\\ 0\end{array}\right)$ and $\left(\begin{array}{c}1\\ 0\\ 1\end{array}\right)$.

Calculate the angle between the vectors $\mathbf{u}=\left(\begin{array}{c}1\\ 2\\ -1\end{array}\right)$ and $\mathbf{v}=\left(\begin{array}{c}3\\ -1\\ 4\end{array}\right)$.

Determine the angle between the vectors $\mathbf{a}=\left(\begin{array}{c}-1\\ 2\\ 2\end{array}\right)$ and $\mathbf{b}=\left(\begin{array}{c}3\\ -6\\ 1\end{array}\right)$.

Determine the angle between the vectors $\mathbf{u}=\left(\begin{array}{c}3\\ 4\end{array}\right)$ and $\mathbf{v}=\left(\begin{array}{c}4\\ -3\end{array}\right)$.

Find the angle between the vectors $\mathbf{u}=\left(\begin{array}{c}1\\ 0\end{array}\right)$ and $\mathbf{v}=\left(\begin{array}{c}0\\ 1\end{array}\right)$.

Find the value of $t$ such that the vectors $\left(\begin{array}{c}t\\ 1\\ 2\end{array}\right)$ and $\left(\begin{array}{c}1\\ t\\ 3\end{array}\right)$ are perpendicular.