Angle Between Two Planes
• The angle between any two planes is same as the angle between their normals.
If the equations of two planes are known then the expression of the angle between the planes can be expressed in vector as well as in Cartesian form.
• If two planes are perpendicular, then the angle between their normals is 90°. Therefore, the dot product of the normal vectors of the planes should be zero. Using this, the condition for perpendicularity is found out.
• If two planes are parallel, then the angle between their normals is 0°. Therefore, the one of the normal vectors can be expressed in terms of another normal vector. Using this, the condition for two vectors being parallel is found out.
• The angle between a line and a plane is the complement angle between the line and the normal to the plane.
Keywords: Angle between two planes, Distance of a point from a plane, Angle between a line and a plane, Condition for perpendicularity of two planes, Condition for two planes to be parallel.
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Q1
Find the distance between the planes x+yz+8=0 and x+ yz=16.
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Q5
Write the value of in the vector form, if is the angle between the two planes , and
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