Q. 1 D

# Find the equation of the plane passing through the following points:

(2, 3, 4), (– 3, 5, 1) and (4, – 1, 2)

Answer :

If the given points are then the equation of the plane passing through these three points is given by the following equation.

Now substitute the values given

Now apply the determinant

(x – 2)(– 4 – 12) – (y – 3)(10 + 6) + (z – 4)(20 – 4) = 0

(x – 2)(– 16) – (y – 3)(16) + (z – 4)(16) = 0

– 16x + 32 – 16y + 48 + 16z – 64 = 0

– 16x – 16y + 16z + 16 = 0

(x + y – z – 1) × – 16 = 0

The equation of plane is

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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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