Daily Practice Problems

Class 11 Maths

Introduction to Three Dimensional Geometry

Class 11 Maths

Introduction to Three Dimensional Geometry

**Question 1:**

Locate the following points in the space.

(i) (1, -1, 3) (ii) (-1, 2, 4)

(iii) (-2, -4, -7) (iv) (-4, 2, -5)

**Question 2:**

How far apart are the points (2, 0, 0) and (-3, 0, 0)?

**Question 3:**

Find the third vertex of triangle whose centroid is origin and two vertices are (2,4,6) and (0, -2, -5).

**Question 4:**

Given that P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which Q divides PR.

**Question 5:**

The distance of point P(3, 4, 5) from the yz-plane is

(a) 3 units

(b) 4 units

(c) 5 units

(d) 550 units

**Question 6:**

If the distance between the points (a, 0, 1) and (0, 1, 2) is √27, then what is the value of a?

**Question 7:**

Three consecutive vertices of a parallelogram ABCD are A(6, -2, 4), B(2, 4, -8) and C(-2, 2, 4). Find the coordinates of the fourth vertex.

**Question 8:**

Show that the triangle ABC with vertices A(0, 4, 1), B(2, 3, -1) and C(4, 5, 0) is right angled.

**Question 9:**

Find the equation of the set of points which are equidistant from the points

(1, 2, 3) and (3, 2, –1).

**Question 10:**

Find the co ordinate of the point which divides the join of P(2, -1, 4) and Q(4, 3, 2) in the ratio 2 : 5 (i) internally (ii) externally.

**Question 11:**

x = a represents a plane parallel to ____.

**Question 12:**

The equation of z-axis, are ______.

**Question 13:**

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (–2, 4, 7) and (3, –5, 8).

**Question 14:**

What are the coordinates of the vertices of a cube whose edge is 2 units, one of whose vertices coincides with the origin and the three edges passing through the origin, coincides with the positive direction of the axes through the origin?

**Question 15:**

Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0).

**Question 16:**

Show that, if x^{2} + y^{2} = 1, then the point {x, y, √(1 - x^{2} - y^{2})} is at a distance unit from the origin.

**Question 17:**

Let A, B, C be the feet of perpendiculars from a point P on x, y, z-axis respectively. Find the coordinates of A, B and C in each of the following where the P is (i) (3, 4, 2) (ii) (– 5, 3, 7) (iii) (4, – 3, – 5)

**Question 18:**

If a parallelepiped is formed by planes drawn through the points (5, 8, 10) and (3, 6, 8) parallel to the coordinate planes, then the length of diagonal of the parallelepiped is __________.

**Question 19:**

The length of the longest piece of a string that can be stretched straight in a rectangular room whose dimensions are 10, 13 and 8 units are _____.

**Question 20:**

The locus of a point for which y = 0, z = 0 is

(a) equation of x-axis

(b) equation of y-axis

(c) equation of z-axis

(d) None of these

**************

**Application of Knowledge:**Problem-solving allows you to apply the theoretical concepts of the topic Class 11 Maths Introduction to 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 11 Maths Introduction to 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 Introduction to Three Dimensional Geometry Class 11 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 Introduction to Three Dimensional Geometry Class 11 Maths Notes on LearnoHub.com**Boosting Confidence:**Successfully solving problems after learning a theoretical concept boosts your confidence in your abilities to handle Introduction to 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 Introduction to Three Dimensional Geometry Class 11 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 Introduction to Three Dimensional Geometry Class 11 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 11 Maths Introduction to 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 11 Maths Introduction to Three Dimensional Geometry NCERT Chapter 11 useful.

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