Exercise 1.1.25

Question

Draw vectors $u, v, w$ so that their combinations $c u+d v+e w$ fill only a line. Find vectors $\boldsymbol{u}, \boldsymbol{v}, \boldsymbol{w}$ so that their combinations $c \boldsymbol{u}+d \boldsymbol{v}+e \boldsymbol{w}$ fill only a plane.

Prakash Anand · Accepted Answer

(a) For a line, choose $u=v=w=$ any nonzero vector\par
(b) For a plane, choose $u$ and $v$ in different directions. A combination like $w=u+v$ is in the same plane.

Exercise 1.1.25

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Exercise 1.1.25

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