मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी विज्ञान (सामान्य) इयत्ता १२ वी

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x + 6y – 3z = 63.

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प्रश्न

Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x + 6y – 3z = 63.

बेरीज
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उत्तर

Given equation of plane is 2x + 6y – 3z = 63.

∴ The direction ratios of the normal to the plane 2x + 6y – 3z = 63 are 2, 6, – 3

∴ Direction cosines are,

l = `2/sqrt(2^2 + 6^2 + (-3)^2`

m = `6/sqrt(2^2 + 6^2 + (-3)^2`

n = `(-3)/sqrt(2^2 + 6^2 + (-3)^2`

∴ l = `2/7, m = 6/7, n = (-3)/7`

The normal form of the plane is

`2/7x + 6/7y - 3/7z = 63/7`

∴ `2/7x + 6/7y - 3/7z` = 9

The co-ordinates of the foot of the perpendicular are

(lp, mp, np) = `[(2/7)9, (6/7)9, ((-3)/7)9]`

= `(18/7, 54/7, (-27)/7)`

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पाठ 6: Line and Plane - Exercise 6.3 [पृष्ठ २१६]
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