Exercise 1.1.20

Question

Locate $\frac12 u + \frac13 v + \frac13 w$ and $\frac12 u + \frac12 w$ in Figure 1.5b. Challenge problem: Under what restrictions on $c, d, e$, will the combinations $cu + dv + ew$ fill in the dashed triangle? To stay in the triangle, one requirement is $c, d, e \geq 0$.

Prakash Anand · Accepted Answer

(a) $\frac{1}{3} \boldsymbol{u}+\frac{1}{3} \boldsymbol{v}+\frac{1}{3} \boldsymbol{w}$ is the center of the triangle between $\boldsymbol{u}, \boldsymbol{v}$ and $\boldsymbol{w} ; \frac{1}{2} \boldsymbol{u}+\frac{1}{2} \boldsymbol{w}$ lies between $\boldsymbol{u}$ and $\boldsymbol{w} \quad$\par

(b) To fill the triangle $\operatorname{keep} c \geq 0, d \geq 0, e \geq 0$, and $c+d+e=1$.

Exercise 1.1.20

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Exercise 1.1.20

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