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Length of perpendicular from a point with position vector \hat{i}+\hat{j}+\hat{k} to the plane \vec{r}\cdot(2\hat{i}+\hat{j}-2\hat{k})=4 is

  • Option 1)

    1 unit

  • Option 2)

    2 units

  • Option 3)

    3 units

  • Option 4)

    4 units

 

Answers (1)

best_answer

As we have learned

Distance of a point from plane(vector form) -

The length of perpendicular from P(a) to the plane

\vec{r}\cdot \vec{n}= d is given by \frac{\left | \vec{a}\cdot \vec{n}-d \right |}{\left | \vec{n} \right |}

-

 

 Here \vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{n}=2\hat{i}+\hat{j}-2\hat{k},d=4

\therefore Perpendicular's length =\frac{|\vec{a}\cdot\vec{n}-d|}{|\vec{n}|}=\frac{|1-4|}{3}=1


Option 1)

1 unit

Option 2)

2 units

Option 3)

3 units

Option 4)

4 units

Posted by

Himanshu

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