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  • Need explanation for: - Three Dimensional Geometry - JEE Main-3

If angle between planes \vec{r}\cdot(3\hat{i}-6\hat{j}+2\hat{k})=4 and \vec{r}\cdot(2\hat{i}-2\hat{j}-\hat{k})=7 is \theta then cos\theta equals 

  • Option 1)

    \frac{16}{21}

  • Option 2)

    \frac{17}{21}

  • Option 3)

    \frac{19}{21}

  • Option 4)

    \frac{13}{21}

 

Answers (1)

best_answer

As we learned

Angle between two planes (vector form) -

Let the two planes be  \vec{r}\cdot \vec{n}= d\: and\: \vec{r}\cdot \vec{n_{1}}= d_{1} then the angle between them is defined as the andgle between their normals

\cos \Theta = \frac{\vec{n}\cdot \vec{n_{1}}}{\left | \vec{n} \right |\left | \vec{n_{1}} \right |}

-

 

 Here, \vec{n}=3\hat{i}-6\hat{j}+2\hat{k} and \vec{n_1}=2\hat{i}-2\hat{j}-\hat{k}

\therefore cos\theta=\frac{\vec{n}\cdot{n_1}}{|\vec{n}||\vec{n_1}|}=\frac{6+12-2}{\sqrt{49}\sqrt{9}}=\frac{16}{21}


Option 1)

\frac{16}{21}

Option 2)

\frac{17}{21}

Option 3)

\frac{19}{21}

Option 4)

\frac{13}{21}

Posted by

Himanshu

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