Q. 105.0( 1 Vote )

# Find the vector equation of the plane which is at a distance of from the origin and its normal vector from the origin is . Also, find its Cartesian form.

Answer :

Given, normal vector

Now,

The equation of the plane in normal form is

…… (i)

(where d is the distance of the plane from the origin)

Substituting and d = in (i)

……(ii)

Cartesian Form

For Cartesian Form, substituting in (ii), we get

So, 2x – 3y + 4z = 6, is the Cartesian form

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Find the equation of the plane which contains the line of intersection of the planes

and

and whose intercept on the x-axis is equal to that of on y-axis.

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