# The coordinates of the foot of the perpendicular from the point (1, −2, 1) on the plane containing the lines  and is Option 1) (2, −4, 2) Option 2) (−1, 2, −1) Option 3)  (0, 0, 0) Option 4) (1, 1, 1)

As we learnt in

Cartesian equation of plane passing through a given point and normal to a given vector -

- wherein

Putting in

We get

First, we find the equation of plane normal vector of plane containing  and is

Unit vector

Hence, equation of plane is of the form

It passes through (-1,1,3)

So plance is

Foot of perpendicular is (0,0,0)

Option 1)

(2, −4, 2)

This option is incorrect

Option 2)

(−1, 2, −1)

This option is incorrect

Option 3)

(0, 0, 0)

This option is correct

Option 4)

(1, 1, 1)

This option is incorrect

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