Important Questions for Class 12 Maths Chapter 11 – Three Dimensional Geometry

Ans –

Ans –

3) What is the angle between the equations 2x = 3y = -z and 6x = -y = -4z?

Ans – Let the angle be θ,

Ans – Let Q be the image of the point P(3, −2, 1) onto the plane defined by the equation 3x − y + 4z = 2.
PQ is perpendicular to the plane.
The direction ratios of line segment PQ are 3, 1, and 4.

The point Q can be expressed as Q(3k + 3, −k − 2, 4k + 1).
The midpoint of PQ lies on the plane given by the equation 3x − y + 4z = 2.

5) Find the equation of a line that passes through the point (2, 0, 5) and is parallel to the line given by the equations 6x – 2 = 3y + 1 = 2z – 2.

Ans – The equation of the line can be expressed as,

The required plane’s equation can be expressed as

6) Verify the coplanarity of the below lines.

Determine the equation of the plane that contains the coplanar lines.

Ans – Given lines are

Compare the lines with,

Through comparison with them, we obtain

By checking the coplanarity of the lines we get

NCERT Questions for Class 12 Maths Chapter 11 – Three Dimensional Geometry

Three Dimensional Geometry is one of the most important chapters in Class 12 Mathematics. The concepts include direction cosines, direction ratios, equations of lines and planes, and the angle between them. To help you prepare well, we have prepared Three Dimensional Geometry Class 12 Important Questions covering all key concepts, including solved examples and exam-focused problems. These questions will strengthen your understanding and improve problem-solving skills.

Importance of Three Dimensional Geometry in Class 12 Maths

Mathematics is a vital subject that deals with the study of shapes and figures in three-dimensional space with Three Dimensional Geometry. This helps the students in understanding spatial relationships between objects and it can quite easily visualize complex structures. With mastery of Three Dimensional Geometry, a student enhances his problem-solving skills along with improving his spatial reasoning skill and solidifies his concepts on geometry further.

Importance of Practicing Important Questions

Solving important questions is one of the prime requisites before the exams as it helps identify the key topics, get well aware of the exam pattern, and develops time management skill too. Students will get an idea by solving important questions about how much they can do and what subject areas they are facing. Important questions are also repeated in the exam; hence, a great tool for scoring high marks.