Area of a Triangle and Equation of a Plane JEE Notes | EduRev

Mathematics (Maths) Class 12

JEE : Area of a Triangle and Equation of a Plane JEE Notes | EduRev

The document Area of a Triangle and Equation of a Plane JEE Notes | EduRev is a part of the JEE Course Mathematics (Maths) Class 12.
All you need of JEE at this link: JEE

D. AREA OF A TRIANGLE
Show that the area of a triangle whose vertices are the origin and the points Area of a Triangle and Equation of a Plane JEE Notes | EduRev and Area of a Triangle and Equation of a Plane JEE Notes | EduRev

The direction ratios of OA are Area of a Triangle and Equation of a Plane JEE Notes | EduRev

Also OA Area of a Triangle and Equation of a Plane JEE Notes | EduRev

and OB Area of a Triangle and Equation of a Plane JEE Notes | EduRev

∴ the d.c.’ s of OA are Area of a Triangle and Equation of a Plane JEE Notes | EduRev

and the d.c.’s of OB are Area of a Triangle and Equation of a Plane JEE Notes | EduRev

 

Hence if θ is the angle between the line OA and OB, then

sin θ Area of a Triangle and Equation of a Plane JEE Notes | EduRev


Hence the area of ΔOAB

Area of a Triangle and Equation of a Plane JEE Notes | EduRev


Ex.6 Find the area of the triangle whose vertices are A(1, 2, 3), B(2, –1, 1)and C(1, 2, –4).

Sol. Let Δx, Δy, Δz be the areas of the projections of the area Δ of triangle ABC on the yz, zx and xy-planes respectively. We have

Δx =Area of a Triangle and Equation of a Plane JEE Notes | EduRev

Δy =Area of a Triangle and Equation of a Plane JEE Notes | EduRev


Δz =Area of a Triangle and Equation of a Plane JEE Notes | EduRev

∴ the required area Δ = Area of a Triangle and Equation of a Plane JEE Notes | EduRev

Ex.7 A plane is passing through a point P(a, –2a, 2a), Area of a Triangle and Equation of a Plane JEE Notes | EduRev at right angle to OP, where O is the origin to meet the axes in A, B and C. Find the area of the triangle ABC.


Sol. OP Area of a Triangle and Equation of a Plane JEE Notes | EduRev

Equation of plane passing through P(a, –2a, 2a) is
A(x – a) + B(y + 2a) + C(z – 2a) = 0.
∵ the direction cosines of the normal OP to the plane ABC are proportional to a – 0, –2a – 0, 2a – 0 i.e. a, –2a, 2a. ⇒ equation of plane ABC is

a(x – a) – 2a(y + 2a) + 2a(z – 2a) = 0 or ax – 2ay + 2az = 9a2 ....(1)

Now projection of area of triangle ABC on ZX, XY and YZ planes are the triangles AOC, AOB and BOC respectively.

Area of a Triangle and Equation of a Plane JEE Notes | EduRev
Area of a Triangle and Equation of a Plane JEE Notes | EduRevArea of a Triangle and Equation of a Plane JEE Notes | EduRev
Area of a Triangle and Equation of a Plane JEE Notes | EduRev
Area of a Triangle and Equation of a Plane JEE Notes | EduRev

Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

Related Searches

Important questions

,

Exam

,

Sample Paper

,

Area of a Triangle and Equation of a Plane JEE Notes | EduRev

,

Viva Questions

,

ppt

,

Previous Year Questions with Solutions

,

Area of a Triangle and Equation of a Plane JEE Notes | EduRev

,

Semester Notes

,

video lectures

,

MCQs

,

Summary

,

Extra Questions

,

shortcuts and tricks

,

mock tests for examination

,

study material

,

Objective type Questions

,

pdf

,

past year papers

,

Free

,

Area of a Triangle and Equation of a Plane JEE Notes | EduRev

,

practice quizzes

;