Question Type 6: Finding the distance between more difficult position vectors Bootcamps

Given the standard basis $\mathbf{a}=(1,0,0)$, $\mathbf{b}=(0,1,0)$, $\mathbf{c}=(0,0,1)$, find the distance between $\mathbf{a}+\mathbf{b}+\mathbf{c}$ and $-(\mathbf{a}-\mathbf{b}+2\mathbf{c})$

Let $\mathbf{a}=(2,2,2)$, $\mathbf{b}=(1,-1,0)$ and $\mathbf{c}=(0,3,-3)$. Find the distance between $\mathbf{a}-\mathbf{c}$ and $\mathbf{b}+2\mathbf{c}$

Given $\mathbf{a}=(1,1,3)$, $\mathbf{b}=(1,0,-1)$ and $\mathbf{c}=(1,1,1)$, find the distance between $\mathbf{a}+\mathbf{b}+\tfrac12\mathbf{c}$ and $-2(\mathbf{a}+\mathbf{b}+\mathbf{c})$

Given $\mathbf{a}=(1,1,1)$, $\mathbf{b}=(2,3,4)$ and $\mathbf{c}=(5,6,7)$, find the distance between $\mathbf{a}+\mathbf{b}+\mathbf{c}$ and $4\mathbf{a}-\mathbf{b}-2\mathbf{c}$

Given $\mathbf{a}=(1,2,3)$, $\mathbf{b}=(4,-1,2)$ and $\mathbf{c}=(0,1,1)$, find the distance between $\tfrac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{2}$ and $\mathbf{b}-2\mathbf{c}+\mathbf{a}$

Let $\mathbf{a}=(3,3,3)$, $\mathbf{b}=(-1,0,2)$ and $\mathbf{c}=(0,1,-1)$. Find the distance between $\mathbf{a}-\mathbf{b}+2\mathbf{c}$ and $-3\mathbf{a}+\mathbf{b}-\mathbf{c}$

Given $\mathbf{a}=(1,4,-2)$, $\mathbf{b}=(-2,1,3)$ and $\mathbf{c}=(3,0,1)$, find the distance between $\mathbf{a}+\mathbf{b}-\mathbf{c}$ and $-\mathbf{a}+2\mathbf{b}+\mathbf{c}$

Let $\mathbf{a}=(2,-1,4)$, $\mathbf{b}=(0,3,1)$ and $\mathbf{c}=(-1,2,2)$. Find the distance between $2\mathbf{a}-\mathbf{b}+\mathbf{c}$ and $\mathbf{a}+3\mathbf{b}-\tfrac14\mathbf{c}$

Given $\mathbf{a}=(3,-1,2)$, $\mathbf{b}=(1,1,1)$ and $\mathbf{c}=(-2,2,0)$, find the distance between $\mathbf{a}+\tfrac13\mathbf{b}-\mathbf{c}$ and $-2\mathbf{a}+\mathbf{b}+\mathbf{c}$

Let $\mathbf{a}=(0,2,4)$, $\mathbf{b}=(5,1,-1)$ and $\mathbf{c}=(2,-2,3)$. Find the distance between $3\mathbf{a}-\tfrac12\mathbf{b}+\mathbf{c}$ and $\mathbf{a}+\mathbf{b}-2\mathbf{c}$

Let $\mathbf{a}=(4,1,0)$, $\mathbf{b}=(0,-3,2)$ and $\mathbf{c}=(5,1,-1)$. Find the distance between $\tfrac{2\mathbf{a}+\mathbf{b}-\mathbf{c}}{3}$ and $\mathbf{a}-2\mathbf{b}+\tfrac12\mathbf{c}$

Let $\mathbf{a}=(-2,0,1)$, $\mathbf{b}=(3,2,-1)$ and $\mathbf{c}=(1,-1,2)$. Find the distance between $-\mathbf{a}+\tfrac32\mathbf{b}-\mathbf{c}$ and $2\mathbf{a}-\mathbf{b}+\tfrac12\mathbf{c}$