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  • Equation of plane given <img alt="\vec{r}\cdot(-3\hat{i}-6\hat{j}+2\hat{k})=-21" src="https://learn.careers360.com/latex-image/?%5Cvec%7Br%7D%5Ccdot%28-3%5Chat%7Bi%7D-6%5Chat%7Bj%7D&plus;2

Equation of plane given \vec{r}\cdot(-3\hat{i}-6\hat{j}+2\hat{k})=-21 in normal form will be 

Option: 1

\vec{r}\cdot(\frac{3}{7}\hat{i}+\frac{6}{7}\hat{j}-\frac{2}{7}\hat{k})=-3


Option: 2

\vec{r}\cdot(\frac{3}{7}\hat{i}+\frac{6}{7}\hat{j}-\frac{2}{7}\hat{k})=3


Option: 3

\vec{r}\cdot(3\hat{i}+6\hat{j}-2\hat{k})=21


Option: 4

\vec{r}\cdot(3\hat{i}-6\hat{j}+2\hat{k})=21


Answers (1)

best_answer

As we have learned

Conversion of equation in normal form (vector form ) -

The equation \vec{r}\cdot \vec{n}= D   is converted in normal by divding it by \left | \vec{n} \right |

\frac{\vec{r}\cdot \vec{n}}{\left | \vec{n} \right |}= \frac{D}{\left | \vec{n} \right |}    

we get     \vec{r}\cdot \hat{n}= d

 

-

 

 Given form is \vec{r}\cdot\vec{n}=-D, firstly making R.H.S positive & then dividing both sides by |\vec{n}| we get required result 

Posted by

Suraj Bhandari

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