The dot product of two vectors $\textbf{A}$ and $\textbf{B}$ is given by

$$\textbf{A}.\textbf{B}=ABcos\theta$$

where A and B are the magnitudes of the vectors $\textbf{A}$ and $\textbf{B}$ respectively and $\theta$ is the angle between the vectors $\textbf{A}$ and $\textbf{B}$.

In short, the dot product of $\textbf{A}$ with $\textbf{B}$ picks out the right component of $\textbf{B}$ in the direction of $\textbf{A}$.

Let

$$\textbf{A}=A_x\hat{x}+A_y\hat{y}+A_z\hat{z}$$ and

$$\textbf{B}=B_x\hat{x}+B_y\hat{y}+B_z\hat{z}$$

then

$$\textbf{A}.\textbf{B}= A_xB_x+A_yB_y+A_zB_z=ABcos\theta$$

The dot product of two vectors is a scalar quantity. For the dot product of two non-zero vectors to be zero, the two vectors should be orthogonal (perpendicular in the Cartesian sense). i.e., $\textbf{A}$ and $\textbf{B}$ should be independent so that they share no common components with each other.

If you increase the magnitude of the vectors or the length of the vectors, then the corresponding components of each vectors increase in the magnitude and since you have only increase the magnitude, the angle between them, $\theta$, will not vary. So the dot product should increase. If you change the vectors so that the angle between them also decrease, then the dot product decreases.

The dot product of two vectors $\textbf{A}$ and $\textbf{B}$ is given by

$$\textbf{A}.\textbf{B}=ABcos\theta$$

where $A$ and $B$ are the magnitudes of the vectors $\textbf{A}$ and $\textbf{B}$, respectively, and $\theta$ is the angle between the vectors $\textbf{A}$ and $\textbf{B}$.

In short, the dot product of $\textbf{A}$ with $\textbf{B}$ picks out the right component of $\textbf{B}$ in the direction of $\textbf{A}$.

Let

$$\textbf{A}=A_x\hat{x}+A_y\hat{y}+A_z\hat{z}$$ and

$$\textbf{B}=B_x\hat{x}+B_y\hat{y}+B_z\hat{z}$$

Then

$$\textbf{A}.\textbf{B}= A_xB_x+A_yB_y+A_zB_z=ABcos\theta$$

The dot product of two vectors is a scalar quantity. For the dot product of two non-zero vectors to be zero, the two vectors should be orthogonal (perpendicular in the Cartesian sense). I.e., $\textbf{A}$ and $\textbf{B}$ should be independent so that they share no common components with each other.

If you increase the magnitude of the vectors or the length of the vectors, then the corresponding components of each vector increase in magnitude. Since you have only increased the magnitude, the angle between them, $\theta$, will not vary. So the dot product should increase. If you change the vectors so that the angle between them also decrease, then the dot product decreases.