Question

Let $\overrightarrow{A}=5\overrightarrow{i}-4\overrightarrow{j}and\overrightarrow{B}=-7·5\overrightarrow{i}+6\overrightarrow{j}$. Do we have $\overrightarrow{B}=k\overrightarrow{A}$? Can we say $\frac{\overrightarrow{B}}{\overrightarrow{A}}$ = k?

Answer 1

If $\overrightarrow{A}=5\overrightarrow{i}-4\overrightarrow{j}\mathrm{and}\overrightarrow{B}=-7·5\overrightarrow{i}+6\overrightarrow{j}$, then we have $\overrightarrow{B}=k\overrightarrow{A}$ by putting the value of scalar k as $-1.5$.
However, we cannot say that $\frac{\overrightarrow{B}}{\overrightarrow{A}}$ = k, because a vector cannot be divided by other vectors, as vector division is not possible.