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In the Following Cases, Find the Coordinates of the Foot of the Perpendicular Drawn from the Origin.2x + 3y + 4z – 12 = 0 - Mathematics

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin.

2x + 3y + 4z – 12 = 0

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Solution

Let the coordinates of the foot of perpendicular P from the origin to the plane be (x1y1z1).

2x + 3y + 4z − 12 = 0

⇒ 2x + 3y + 4z = 12 … (1)

The direction ratios of normal are 2, 3, and 4

`:. sqrt((2)^2 + (3)^2 + (4)^2) =  sqrt29`

Dividing both sides of equation (1) by sqrt29, we obtain

This equation is of the form lx + my + nz = d, where lmn are the direction cosines of normal to the plane and d is the distance of normal from the origin.

The coordinates of the foot of the perpendicular are given by

(ldmdnd).

Therefore, the coordinates of the foot of the perpendicular are

Concept: Vector and Cartesian Equation of a Plane
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APPEARS IN

NCERT Class 12 Maths
Chapter 11 Three Dimensional Geometry
Q 4.1 | Page 493
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