Question

the foot of the perpendicular drawn from the origin to a plane M(2,1,-2) vector the equation of the plane​

Answer 1

SOLUTION

GIVEN

The foot of the perpendicular drawn from the origin to a plane M(2,1,-2) vector

TO DETERMINE

The the equation of the plane

EVALUATION

Here it is given that the foot of the perpendicular drawn from the origin to a plane M(2,1,-2) vector

So by the given condition

$\vec{a} = 2 \hat{i} + \hat{j} - 2 \hat{k}$

$\vec{n} = 2 \hat{i} + \hat{j} - 2 \hat{k}$

So the required equation of the plane is

$\vec{r}.\vec{n} =\vec{a}.\vec{n}$

$\implies \: (x \hat{i} + y\hat{j} + z \hat{k}).(2 \hat{i} + \hat{j} - 2 \hat{k} )=(2 \hat{i} + \hat{j} - 2 \hat{k}).( 2 \hat{i} + \hat{j} - 2 \hat{k}) \:$

$\implies \: 2x + y - 2z=4 + 1 + 4 \:$

$\implies \: 2x + y - 2z=9$

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