Question Type 2: Finding the angle between two different vectors Exercises

Find the angle between the vectors $u=(1,0)$ and $v=(0,1)$.

Determine the angle between the vectors $u=(3,4)$ and $v=(4,-3)$.

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

Calculate the angle between the vectors $(1,4,3)$ and $(2,1,2)$.

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

Determine the angle between the vectors $(1,1,0)$ and $(1,0,1)$.

Calculate the angle between the vectors $(2,-1,2)$ and $(1,2,3)$.

Calculate the angle between $\mathbf{u}=\langle1,2,-1\rangle$ and $\mathbf{v}=\langle3,-1,4\rangle$.

Determine the angle between the vectors $(-1,2,2)$ and $(3,-6,1)$.

Find the angle between the vectors $(4,1,-4)$ and $(1,-2,2)$.

Find the value(s) of $t$ such that the angle between the vectors $(1,0,t)$ and $(0,1,1)$ is $60^\circ$.

Find the value of $t$ such that the vectors $(t,1,2)$ and $(1,t,3)$ are perpendicular.

Let $\mathbf{a}$ and $\mathbf{b}$ be vectors with $|\mathbf{a}|=4$, $|\mathbf{b}|=3$ and $\mathbf{a}\cdot\mathbf{b}=6$. Find the angle between $\mathbf{a}+\mathbf{b}$ and $\mathbf{a}-\mathbf{b}$.