Three Dimensional Geometry

Board: JEE Main |Exam:JEEMain

JEEMainstudynotesforThreeDimensionalGeometrybyAjayYadav.

KeyConcepts

DirectionCosines/Ratios

l²+m²+n²=1.DRproportionaltol,m,n.

Lines

Equation:vectorr=a+λb,cartesian(x-x₁)/a=(y-y₁)/b=(z-z₁)/c.Anglebetweenlines,shortestdistance.

Planes

ax+by+cz+d=0.Intercept:x/p+y/q+z/r=1.Anglebetweenplanes.Distancefrompoint.Familyofplanes.

Sphere

(x-a)²+(y-b)²+(z-c)²=r².Tangentplane.Greatcircle.

ImportantFormulas

DCsumsq	l²+m²+n²=1
Lineeq	(x-x₁)/a=(y-y₁)/b=(z-z₁)/c
Planeeq	ax+by+cz+d=0

SolvedExamples

Example1:Finddistancefrom(1,2,3)to2x+3y+4z-20=0.

Solution:|2+6+12-20|/√4+9+16=0/√29=0.

Practice Questions

1. Find angle between lines (x-1)/2=(y+2)/3=(z-3)/4 and x/5=(y-1)/6=(z+2)/7.
2. Find equation of plane through (1,2,3) with normal DR (2,-1,3).
3. Find SD between skew lines.
4. Find image of (1,2,3) in plane 2x-y+z=5.
5. Find equation of sphere with center (1,2,3) and radius 4.

Download PDF

Download PDF notes.