Question Type 4: Determining if combinations of the specific vectors are parallel, perpendicular or neither Bootcamps

Are the vectors $2a + 3b$ and $-4a - 6b$ parallel, perpendicular, or neither? Here $a=(1,3,4)$ and $b=(1,0,1)$.

Determine whether the vectors $a + 2c$ and $4b - c$ are parallel, perpendicular, or neither, where $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

Determine whether the vector $2a - 3b$ is parallel, perpendicular, or neither to the vector $a + b$, where $a=(1,3,4)$ and $b=(1,0,1)$.

Determine if the vectors $a + 2b - c$ and $2a - 4b + 2c$ are parallel, perpendicular, or neither. Here $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

Is the vector $a + b + c$ parallel to $b + 2c$? Use $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

Are the vectors $a - 3b + c$ and $-2a + 6b - 2c$ parallel, perpendicular, or neither? Use $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

Check if the vector $3a - b + c$ is perpendicular to $a - 2c$, where $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

Determine if the vector $5a - 2c$ is perpendicular to $2a + b$, given $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

Decide whether $a - b + 2c$ and $3a + 6b - 4c$ are parallel, perpendicular, or neither, where $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

Check if $4a - b + c$ is orthogonal to $a + 3b - 2c$, where $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

Is the vector $a + (b + c)$ perpendicular or parallel to $a - (b - c)$, given $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$?

Check if $3(a - b) + 4c$ is parallel, perpendicular, or neither to $-6(a - b) - 8c$, where $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.