Two vectors $\vec{A}$ and $\vec{B}$ are at right angles to each other,when

Define the vector product of two vectors.

Find the component of vector $\vec{r}$ in the direction of vector $\vec{a}$.

If $\vec{a}$ and $\vec{b}$ make an angle $\cos^{-1}\left(\frac{5}{9}\right)$ with each other,then $|\vec{a}+\vec{b}|=\sqrt{2}|\vec{a}-\vec{b}|$ for $|\vec{a}|=n|\vec{b}|$. The integer value of $n$ is . . . . . . .

In a right-handed Cartesian coordinate system (often referred to as a clockwise system when viewed from the positive axis),which of the following vector relations is correct?

If $A = a_1 \hat{i} + b_1 \hat{j}$ and $B = a_2 \hat{i} + b_2 \hat{j}$,the condition that they are perpendicular to each other is