How the dot product of two vectors can be zero?

Question

I am given,

$\vec s$$=2\hat i+\hat j-3\hat k$

and

$\vec r$$=4\hat i+\hat j+3\hat k$

Now I am asked to calculate the dot product $\vec s\cdot\vec r$ But I am getting $0$ as result.

Is this possible? And if possible, then how can the dot product simply become zero?

Answer 1

$$\vec s.\vec r=(2\hat i+\hat j-3\hat k)\cdot(4\hat i+\hat j+3\hat k)=8+1-9=0$$ that means $\vec s$ and $\vec r$ are perpendicular to each other.the intuition behind this dot product is what amount of $\vec s$ is working along with $\vec r$?If we would get some positive value,then that would mean that there is some component of s along r as it brings us in a conclusion that s would be inclined to r.But we have a zero here,that means no component of s is working along r.it is only possible when vectors are orthogonal.