Exercise 1.1.5

Question

Prove that if the vector $x$ emanates from the origin of the Euclidean plane and terminates at the point with coordinates $\left(a_{1}, a_{2}\right)$, then the vector $t x$ that emanates from the origin terminates at the point with coordinates $\left(t a_{1}, t a_{2}\right)$.

Jephian C.-H. Lin · Accepted Answer

\begin{proof}
Since $x=(a_1,a_2)-(0,0)=(a_1,a_2)$, we have $tx=(ta_1,ta_2)$. Hence the head of that vector will be $(0,0)+(ta_1,ta_2)=(ta_1,ta_2)$.
\end{proof}

Exercise 1.1.5

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Exercise 1.1.5

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