FAQs on Coplanarity of 2 Lines and Angle between 2 Planes - Three Dimensional Geometry, Class 12, Math

Question 1

1. What is the concept of coplanarity in three-dimensional geometry?

Accepted Answer

Ans. Coplanarity refers to the property of points, lines, or vectors lying on the same plane. In the context of two lines in three-dimensional space, if the lines are coplanar, it means they lie on the same plane. This means that the two lines can be contained within a single plane and do not intersect. Conversely, if the lines are not coplanar, they will intersect or be skew lines.

Question 2

2. How can we determine if two lines are coplanar?

Accepted Answer

Ans. To determine if two lines are coplanar, we can use the concept of vector equations. If the direction vectors of the two lines are proportional, then the lines are coplanar. Alternatively, we can find a point that lies on both lines and check if this point, along with the direction vectors of the lines, lies on the same plane. If they do, then the lines are coplanar.

Question 3

3. What is the angle between two planes in three-dimensional geometry?

Accepted Answer

Ans. The angle between two planes in three-dimensional geometry is the angle formed between the normals of the planes. The normal vectors of the two planes are perpendicular to the planes and can be used to determine the angle between them. This angle represents the inclination or deviation of one plane from another.

Question 4

4. How can we calculate the angle between two planes using their normal vectors?

Accepted Answer

Ans. To calculate the angle between two planes using their normal vectors, we can use the dot product formula. Let n1 and n2 be the normal vectors of the two planes. The angle θ between the planes is given by the equation: θ = cos^(-1)(|n1 · n2| / (|n1| * |n2|)), where · represents the dot product and | | represents the magnitude of the vectors.

Question 5

5. How does the angle between two planes relate to the coplanarity of lines?

Accepted Answer

Ans. The angle between two planes is related to the coplanarity of lines because if two lines are coplanar, they lie on the same plane. Therefore, the angle between the two planes containing these lines will be zero degrees. Conversely, if the angle between two planes is zero degrees, it implies that the lines contained in those planes are coplanar. So, the coplanarity of lines can be determined indirectly by analyzing the angle between the planes that contain them.

Coplanarity of 2 Lines and Angle between 2 Planes - Three Dimensional Geometry,

Mathematics for SSS 3

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