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Exercise 1.2.5

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1) We have

u_{1} = \frac{v}{∥ v ∥} = \frac{(1, 3)}{\sqrt{10}}

$U_{1} = (3, - 1) ∕ \sqrt{10}$ is perpendicular to $u_{1}$ (and so is $(- 3, 1) ∕ \sqrt{10})$ .

2) We have

u_{2} = \frac{w}{∥ w ∥} = \frac{(2, 1, 2)}{3} .

$U_{2}$ could be $(1, - 2, 0) ∕ \sqrt{5}$ : There is a whole plane of vectors perpendicular to $u_{2}$ , and a whole circle of unit vectors in that plane.

mathchakra

2021-11-20 14:00

Exercise 1.2.5

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