Question Type 2: Finding the vector equation of a line defined by composite vectors Bootcamps

Let $a=(1,3,4)$, $b=(8,1,1)$ and $c=(0,1,0)$. Find the vector equation of the line through the points $P=a$ and $Q=b$.

Let $a=(1,3,4)$, $b=(8,1,1)$ and $c=(0,1,0)$. Find the vector equation of the line through $P=a+2c$ and parallel to $\mathbf{v}=b-3c$.

Let $a=(1,3,4)$ and $c=(0,1,0)$. Find the vector equation of the line through $P=c-a$ and parallel to $\mathbf{v}=b+c$ where $b=(8,1,1)$.

Let $a=(1,3,4)$ and $b=(8,1,1)$. Find the vector equation of the line through $P=2a-b$ and $Q=a+2b$.

Let $a=(1,3,4)$ and $c=(0,1,0)$. Find the vector equation of the line through $P=a+b$ and $Q=c-2a$ with $b=(8,1,1)$.

Let $a=(1,3,4)$, $b=(8,1,1)$ and $c=(0,1,0)$. Find the vector equation of the line through $P=a+2b$ parallel to $\mathbf{v}=c-3b+a$.

Let $a=(1,3,4)$, $b=(8,1,1)$ and $c=(0,1,0)$. Find the vector equation of the plane through $a,b,c$.

Let $a=(1,3,4)$, $b=(8,1,1)$ and $c=(0,1,0)$. Find the vector equation of the plane containing the points $P=a+b$, $Q=c-2a$ and $R=a+2b+2c$.

Let $a=(1,3,4)$, $b=(8,1,1)$ and $c=(0,1,0)$. Find the vector equation of the plane through $P=2a-b+c$ and parallel to both $\mathbf{u}=b+a$ and $\mathbf{v}=c-a$.

Let $a=(1,3,4)$, $b=(8,1,1)$ and $c=(0,1,0)$. Find the vector equation of the plane through $P=2a-b$, $Q=3b+c$, $R=4c-a$.

Let $a=(1,3,4)$, $b=(8,1,1)$ and $c=(0,1,0)$. Find the vector equation of the plane through $P=a+b-c$, $Q=2a+3b$ and $R=4c$.

Let $a=(1,3,4)$, $b=(8,1,1)$ and $c=(0,1,0)$. Find the vector equation of the plane passing through $P=a-2b+c$, $Q=3a+b-c$, and $R=2b+2c-a$.