Question

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

• 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

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 the 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