Question Type 3: Determining whether two vectors are perpendicular Exercises

Determine whether vectors $a=(1,3,4)$ and $c=(0,1,0)$ are perpendicular.

Determine whether vectors $b=(1,0,1)$ and $c=(0,1,0)$ are perpendicular.

Determine whether vectors $a=(1,3,4)$ and $b=(1,0,1)$ are perpendicular.

For what values of $k$ is the vector $(k^2,k,1)$ perpendicular to $c=(0,1,0)$?

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

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

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

Find the scalar $t$ such that $a+tb$ is perpendicular to $c$, with $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

Find the scalar $s$ such that $sa+c$ is perpendicular to $b$, with $a=(1,3,4)$, $b=(1,0,1)$, $c=(0,1,0)$.

For what values of $k$ is the vector $(k^2,k,1)$ perpendicular to $(1,-2,1)$?

For what values of $k$ is the vector $(k^2,k,1)$ perpendicular to $b=(1,0,1)$?

For what values of $k$ is the vector $(k^2,k,1)$ parallel to $(1,-2,1)$?