NCERT Solutions Class 12 Maths Chapter 11 Miscellaneous Exercise

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Download CBSE NCERT Solutions for Class 12 Maths Chapter 11 Miscellaneous Exercise 11 in PDF file format free or view online in videos format also. Solutions are available in Hindi and English Medium following the latest NCERT Books for class 12 session 2024-25.

A plane is determined uniquely if any one of the following is known:

1. The normal to the plane and its distance from the origin is given, i.e., equation of a plane in normal form.
2. It passes through a point and is perpendicular to a given direction.
3. It passes through three given non collinear points.

Here, we shall discuss vector and Cartesian equations of the planes.

• 1. If d is the distance from the origin and l, m, n are the normal cosines of the plane direction through the origin, the foot of the perpendicular is (ld, md, nd).
• 2. Do you know why was it necessary to say that the three points had to be non collinear? If the three points were on the same line, then there will be many planes that will contain them.
• 3. The angle between two planes is defined as the angle between their normal.
• 4. The planes are perpendicular to each other if n1.n2 = 0 and parallel if n1 is parallel to n2.
• 5. The angle between a line and a plane is the complement of the angle between the line and normal to the plane.

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