Exercise 1.1.17

Question

Locate $\frac{1}{3} v+\frac{1}{3} w$ and $\frac{2}{3} v+\frac{2}{3} w$. The combinations $c v+c w$ fill out what line?

Prakash Anand · Accepted Answer

All vectors $c \boldsymbol{v}+c \boldsymbol{w}$ are on the line passing through $(0,0)$ and $\boldsymbol{u}=\frac{1}{2} \boldsymbol{v}+\frac{1}{2} \boldsymbol{w}$. That line continues out beyond $\boldsymbol{v}+\boldsymbol{w}$ and back beyond $(0,0)$. With $c \geq 0$, half of this line is removed, leaving a ray that starts at $(0,0)$.

Exercise 1.1.17

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Exercise 1.1.17

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