Question Type 3: Finding the angle between vectors Bootcamps

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

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

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

Let $\mathbf{u}=(2,-1,4)$ and $\mathbf{v}=(1,3,-2)$. Find the angle between $\mathbf{u}$ and $\mathbf{v}$.

Find the acute angle between the vectors $(5,-3,1)$ and $(2,4,3)$.

Show whether the angle between the vectors $(1,2,-1)$ and $(4,0,3)$ is acute or obtuse, and find its measure.

Find the angle between the vector sum $(1,2,3)+(4,0,-1)$ and the vector $(2,3,-4)$.

Find the angle between $\mathbf{u}=(1,-1,2)$ and $\mathbf{v}=(-2,4,-1)$.

Given vectors $\mathbf{a}=(1,2,2)$ and $\mathbf{b}=(3,x,5)$ are perpendicular, find $x$ and verify that the angle between them is $90^\circ$.

Determine the angle between $\mathbf{u}=(3,-3,1)$ and $\mathbf{v}=(-1,2,2)$.

Find the value of $x$ such that the angle between the vectors $(x,1,2)$ and $(2,3,4)$ is $60^\circ$.

Let $\mathbf{u}=(\cos\alpha,\sin\alpha,0)$ and $\mathbf{v}=(1,0,1)$. Find $\alpha$ such that the angle between $\mathbf{u}$ and $\mathbf{v}$ is $45^\circ$.