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Question Number 191935 by Rupesh123 last updated on 04/May/23

Answered by som(math1967) last updated on 04/May/23

$$DirectioncosineofL$$$$cos\alpha ,cos\beta ,cos\gamma$$$$\therefore {cos}^2\alpha +{cos}^2\beta +{cos}^2\gamma =1$$$$1-{sin}^2\alpha +1-{sin}^2\beta +1-{sin}^2\gamma =1$$$$\therefore {sin}^2\alpha +{sin}^2\beta +{sin}^2\gamma =3-1=2$$

Answered by mehdee42 last updated on 04/May/23

$${cos}^2\alpha +{cos}^2\beta +{cos}^2\gamma =1\Rightarrow$$$${sin}^2\alpha +{sin}^2\beta +{sin}^2\gamma =2$$$$tip\because cos\alpha =\frac{a}{\mid v\mid }\mathrm{\&}cos\beta =\frac{b}{\mid v\mid }\mathrm{\&}cos\gamma =\frac{c}{\mid v\mid };v=(a,b,c)$$

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