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  • Show that the plane contains the line <img alt="\frac{x-5}{3}=y=2-z" src="https://learn.careers360.com/latex-image/?%5Cfrac%7Bx-5%7D%7B3%7D%3Dy%3D2-z

Show that the planex - 5y -2z = 1 contains the line \frac{x-5}{3}=y=2-z

 

 
 
 
 
 

Answers (1)

Given:

Plane: x - 5y -2z = 1

\vec{r}.(\hat {i}-5\hat {j}-2\hat {k})=1

Direction ratio of the plane \vec{p}= \hat {i}-5\hat {j}-2\hat {k}

Line: \frac{x-5}{3}=y=2-z

\vec{r} = (5\hat {i}+2\hat {k})+\lambda( 3\hat {i} + \hat {j}-\hat {k} )

Direction ratio of the plane \vec{L}= 3\hat {i}+\hat {j}-\hat {k}

\\ \vec{p}\cdot \vec{L}= (\hat {i}-5\hat {j}-2\hat {k})(3\hat {i}+\hat {j}-\hat {k}) \\ = 3-5+2=0

Hence this given plane contain the  given line.

Posted by

Safeer PP

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