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Distance between two parallel planes 2x+y+2z=8\: and \: 4x+2y+4z+5=0 is :

  • Option 1)

    \frac{9}{2}

  • Option 2)

    \frac{3}{2}

  • Option 3)

    \frac{5}{2}

  • Option 4)

    \frac{7}{2}

 

Answers (1)

best_answer

As we learnt in

Distance between parallel planes (vector form ) -

Distance between \vec{r}\cdot \vec{n}= d  and \vec{r}\cdot \vec{n}= d_{1} is given by 

\frac{\left | d_{1} -d\right |}{\vec{n}}

-

 

 4x+2y+4z = 16

4x+2y+4z = -5

d= \frac{16+5}{\sqrt{4^{2}+2^{2}+42}} = \frac{21}{6}= \frac{7}{2}


Option 1)

\frac{9}{2}

This option is incorrect

Option 2)

\frac{3}{2}

This option is incorrect

Option 3)

\frac{5}{2}

This option is incorrect

Option 4)

\frac{7}{2}

This option is correct

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