Angle between two planes - Introduction
Vector Form: If r.n1=d1 and r.n2=d2 are the equation of two planes then angle between them is given by the equation
Cartesian Form: If A1x + B1y + C1z + D1=0 and A2x + B2y + C2z + D2=0 are the Cartesian equations of two planes and θ is the angle between them then
1. If the planes are parallel then
Condition for parallelism and perpendicularity
2. If the planes are perpendicular then A1A2 + B1B2 + C1C2=0
Coplanarity of Two Lines
Vector Form: If r = a1 + λb1 and r= a2 + μb2 are the equations of two lines then they are said to be coplanar if (a2-a1).(b1 x b2)=0
Cartesian Form: If A(x1, y1, z1) and B(x2, y2, z2) are two points with the direction ratios of parallel vectors <a1, b1, c1> and <a2, b2, c2>, then the lines are said to be coplanar if
Distance of a point from a plane
Vector Form: If the equation of the plane is in the form r.N=d, where N is normal to the plane, then the perpendicular distance is
The length of perpendicular from origin O to the plane r.N=d is |d|/|N|
Cartesian Form: If P(x1, y1, z1) be the given point with position vector a and Ax + By + Cz=D be the equation of the plane then the perpendicular distance from P to the plane is given by d=
Angle between a Line and a Plane
If r=a+λb be the equation of the line and r.n=d be the equation of the plane the angle between them is given by
Example: Find the distance of a point (2, 5, -3) from the plane 6x - 3y + 2z - 4=0
Now try it yourself! Should you still need any help, click here to schedule live online session with e Tutor!
About eAge Tutoring:
eAgeTutor.com is the premium online tutoring provider. Using materials developed by highly qualified educators and leading content developers, a team of top-notch software experts, and a group of passionate educators, eAgeTutor works to ensure the success and satisfaction of all of its students.
Contact us today to learn more about our tutoring programs and discuss how we can help make the dreams of the student in your life come true!