Daily Practice Problems
Class 12 Maths
Three Dimensional Geometry
Class 12 Maths
Three Dimensional Geometry
Question1:
The vector equation of the line which passing through the point (3, 4, 5) and parallel to the vector 
is [Level: Moderate]
(a) (
) + 
(
)
(b) (
) + ( )
(c) ( ) + (
)
(d) all of these.
Question2:
The vector 
lies in the plane of the vectors 
and 
and bisects the angle between 
and 
. Then which one of the following gives possible values of 
and 
? [Level: Moderate]
(a) 
(b) 
(c) 
(d) 
Question3:
If direction cosines of two lines are proportional to 
and 
, then the acute angle between them is __________. [Level: Moderate]
Question4:
Direction ratios of two lines are 
and 
, then the lines are [Level: Difficult]
(a) mutually perpendicular
(b) parallel
(c) coincident
(d) none of these.
Question5:
Under what condition do 
represent direction cosines of a line. [Level: Moderate]
(a) 
(b) 
(c) 
(d) For any value of k.
Question6:
The direction cosines 
of two lines are connected by the relations 
, then the angle between them is [Level: Difficult]
(a) 
(b) 
(c) 
(d) 0.
Question7:
The vector equation of the symmetrical form of equation of straight line 
is
[Level: Moderate]
(a) 
(b) 
(c) 
(d) 
.
Question8:
The direction cosines of the line joining the points 
and 
are __________. [Level: Moderate]
Question9:
The projection of line joining 
on the line joining 
&
is __________. [Level: Difficult]
Question10:
The lines 
and 
are coplanar if [Level: Moderate]
(a)
(b)
(c) 
(d) 
.
Question11:
If the co-ordinates of the points P & Q are 
and O be the origin, then [Level: Moderate]
(a) 
(b) 
(c) 
(d) none of these.
Question12.
The distance of the point 
from the line 
is [Level: Moderate]
(a) 
(b) 
(c) 
(d) 
.
Question13.
A line makes angles of 
and 
with the positive X - axis and Y - axis respectively. The angle made by the same line with the positive Z - axis is [Level: Difficult]
(a) 
(b) 
(c) 
(d) 
.
Question14.
If 
are the direction cosines of a line, then the value of n is__________. [Level: Moderate]
Question15.
The projections of the segment PQ on the co-ordinate axes are 
respectively. Then direction cosines of the line PQ are [Level: Moderate]
(a) 
(b) 
(c) 
(d) 
.
Question16.
If a line makes 
with the coordinate axes, then 
is [Level: Moderate]
(a) 0
(b) 1
(c) 2
(d) 3
Question17.
The angle between the lines whose direction cosines are 
and 
is __________. [Level: Moderate]
Question18.
If the straight lines 
and 
are coplanar, then 
is [Level: Difficult]
(a) 
(b) 
(c) 1
(d) 2.
Question19.
The distance between the points P
and Q
is [Level: Easy]
(a) 3
(b) 5
(c) 7
(d) 9.
Question20.
The angle between the lines 2x = 3x = 
and 6x = 
y = 4z is [Level: Difficult]
(a) 90°
(b) 0°
(c) 30°
(d) 45°.
**********
Problem-solving on Class 12 Maths Three Dimensional Geometry NCERT Chapter 11 after learning a theoretical concept is crucial for several reasons:
- Application of Knowledge: Problem-solving allows you to apply the theoretical concepts of the topic Class 12 Maths Three Dimensional Geometry you have learned to real-life situations. It helps you bridge the gap between abstract knowledge and practical scenarios, making the learning more relevant and meaningful.
- Understanding Deeper Concepts: When you encounter problems related to a theoretical concept that you learned in Class 12 Maths Three Dimensional Geometry NCERT Chapter 11, you are forced to delve deeper into its intricacies. This deeper understanding enhances your comprehension of the subject and strengthens your grasp of the underlying principles.
- Critical Thinking: Problem-solving encourages critical thinking and analytical skills. It requires you to analyze the problem, identify relevant information, and devise a logical solution. This process sharpens your mind and improves your ability to approach complex challenges effectively.
- Retention and Recall: Actively engaging in problem-solving reinforces your memory and improves long-term retention. Applying the concepts learned in Three Dimensional Geometry Class 12 Maths in practical scenarios helps you remember them better than passive reading or memorization.
- Identifying Knowledge Gaps: When you attempt to solve problems, you may encounter areas where your understanding is lacking. These knowledge gaps become evident during problem-solving, and you can then focus on filling those gaps through further study and practice. You can refer Three Dimensional Geometry Class 12 Maths Notes on LearnoHub.com
- Boosting Confidence: Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Three Dimensional Geometry. This confidence motivates you to tackle more challenging tasks and improves your overall performance in the subject.
- Preparation for Exams and Challenges: Many exams, especially in science, mathematics, and engineering, involve problem-solving tasks. Regular practice in problem-solving prepares you to face these exams with confidence and perform well. It is also advised to take tests on Three Dimensional Geometry Class 12 Maths Online Tests at LearnoHub.com.
- Enhancing Creativity: Problem-solving often requires thinking outside the box and exploring various approaches. This fosters creativity and innovation, enabling you to come up with novel solutions to different problems.
- Life Skills Development: Problem-solving is a valuable life skill that extends beyond academics. It equips you with the ability to tackle various challenges you may encounter in personal and professional life.
- Improving Decision Making: Problem-solving involves making decisions based on available information and logical reasoning. Practicing problem-solving enhances your decision-making skills, making you more effective in making informed choices.
In summary, problem-solving after learning a theoretical concept on CBSE Three Dimensional Geometry Class 12 Maths is an essential part of the learning process. It enhances your understanding, critical thinking abilities, and retention of knowledge. Moreover, it equips you with valuable skills that are applicable in academic, personal, and professional contexts.
You must have heard of the phrase “Practice makes a man perfect”. Well, not just a man, practice indeed enhances perfection of every individual.
Practicing questions plays a pivotal role in achieving excellence in exams. Just as the adage goes, "Practice makes perfect," dedicating time to solve a diverse range of exam-related questions yields manifold benefits. Firstly, practicing questions allows students to familiarize themselves with the exam format and types of problems they might encounter. This familiarity instills confidence, reducing anxiety and improving performance on the actual exam day. Secondly, continuous practice sharpens problem-solving skills and enhances critical thinking, enabling students to approach complex problems with clarity and efficiency. Thirdly, it aids in identifying weak areas, allowing students to focus their efforts on improving specific topics. Moreover, practice aids in memory retention, as active engagement with the material reinforces learning. Regular practice also hones time management skills, ensuring that students can allocate appropriate time to each question during the exam. Overall, practicing questions not only boosts exam performance but also instills a deeper understanding of the subject matter, fostering a holistic and effective learning experience.
All About Daily Practice Problems on Class 12 Maths Three Dimensional Geometry NCERT Chapter 11
Our Daily Practice Problems (DPPs) offer a diverse range of question types, including Multiple Choice Questions (MCQs) as well as short and long answer types. These questions are categorized into Easy, Moderate, and Difficult levels, allowing students to gradually progress and challenge themselves accordingly. Additionally, comprehensive solutions are provided for each question, available for download in PDF format - Download pdf solutions as well as Download pdf Questions. This approach fosters a holistic learning experience, catering to different learning styles, promoting self-assessment, and improving problem-solving skills. With our well-structured DPPs, students can excel in exams while gaining a deeper understanding of the subject matter. Hope you found the content on Class 12 Maths Three Dimensional Geometry NCERT Chapter 11 useful.
Last but not least, to get the best hold on Class 12 Maths Three Dimensional Geometry NCERT Chapter 11, do not forget to check out:
- Three Dimensional Geometry Class 12 Maths Best videos
- Three Dimensional Geometry Class 12 Maths NCERT Solutions
- Class 12 Maths Three Dimensional Geometry Revision notes
- Three Dimensional Geometry Class 12 Maths DPPs, Download PDF of solutions
- Class 12 Maths Three Dimensional Geometry Online Tests
- Class 12 Maths Sample papers