Question

Find the equation of plane if it passes through a point (2, 3, - 4) and is perpendicular to the line with direction ratios (2,3, -1) .

• A. 2x + 3y - z = 13
• B. 2x + 3y - z = 17
• C. 3x + 2y - z = 13
• D. 3x + 2y - z = 17

Answer 1

The correct option is B

2x + 3y - z = 17

Out of all the forms we have seen to write the equation of plane it is wise to use the point normal form here as we know the coordinates of a point and also the direction cosines of the perpendicular (normal). Equation of plane in point normal form is

$a(x-x_1)+b(y-y_1)+c(z-z_1)=0$

Where a, b, c are the direction ratios of normal and $(x_1,y_1,z_1$) are the coordinates of the point given.

So the equation will be -

2(x - 2) + 3(y -3) -1(z + 4) = 0

Or 2x + 3y - z = 17