Daily Practice Problems
Class 12 Maths
Vector Algebra
Class 12 Maths
Vector Algebra
Question1:
If 
and 
are the two vectors such that 
and 
, then [Level: Moderate]
(a) is parallel to .
(b) is perpendicular to .
(c) either or is a null vector
(d) none of these.
Question2:
If the sum of two unit vectors is a unit vector, then the magnitude of their difference is [Level: Difficult]
(a) 
(b) 
(c) 
(d) 0.
Question3:
The magnitude of each of the two vectors 
and 
, having the same magnitude such that the angle between them is 600 and their scalar product is 
is __________. [Level: Moderate]
Question4:
If 
respectively are the position vectors of points A, B, C and D, then 
are [Level: Difficult]
(a) perpendicular to each other
(b) parallel to each other
(c) neither perpendicular nor parallel to each other
(d) none of these.
Question5:
For any vector , the value of 
is equal to [Level: Difficult]
(a) 
(b) 
(c) 
(d) 
.
Question6:
If 
is the middle point of 
and 
is any point outside , then [Level: Difficult]
(a) 
(b) 
(c) 
(d) 
.
Question7:
The non-zero vectors are 
and 
are related by 
and 
. Then the angle between and is [Level: Moderate]
(a) 0
(b) 
(c) 
(d) 
Question8:
If a line makes angles 90o, 135o, 45o with the x, y and z axes respectively, then its direction cosines are __________. [Level: Moderate]
Question9:
If 
, 
, then a value of 
for which 
is perpendicular to 
is __________. [Level: Moderate]
Question10:
If two vectors 
and 
are such that 
, then [Level: Easy]
(a) they have same magnitude and direction regardless of the positions of their initial points
(b) they have same magnitude and different directions
(c) Both (a) and (b) are true
(d) Both (a) and (b) are false
Question11:
If 
then the vectors and are adjacent sides of [Level: Moderate]
(a) a rectangle
(b) a square
(c) a rhombus
(d) none of these
Question12.
If 
are two non-zero and non-collinear vectors, then 
and 
are [Level: Moderate]
(a) linearly dependent vectors
(b) linearly independent vectors
(c) linearly dependent and independent vectors
(d) none of these
Question13.
If and are two collinear vectors then which of the following are incorrect [Level: Easy]
(a) 
, for some scalar
(b) 
(c) the respective components of are proportional
(d) both the vectors have same direction, but different magnitudes.
Question14.
If 
and 
, then both the vectors and are collinear iff [Level: Moderate]
(a) 
(b) 
(c) 
(d) none of these.
Question15.
If 
is the unit vector along a line l, then the projection of a vector on the line l is given by __________. [Level: Moderate]
Question16.
The area of a triangle with adjacent sides 
is __________. [Level: Easy]
Question17.
If , , 
and 
are four non-zero vectors such that 
= 
and 
= 
, then angle between ( - 2 ) and (2 - ), where 
2 , 2 is __________. [Level: Difficult]
Question18.
In a parallelogram PQRS, 
= 3
- 2
+ 2
and 
= - - 2 . Then |
| is equal to __________. [Level: Moderate]
Question19.
In a parallelogram PQRS, = 3 - 2 + 2 and = - - 2 . Then |
| is equal to __________. [Level: Moderate]
Question20.
If 
, then is [Level: Difficult]
(a) 
(b) 
(c) 
(d) .
**********
Problem-solving on Class 12 Maths Vector Algebra NCERT Chapter 10 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 Vector Algebra 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 Vector Algebra NCERT Chapter 10, 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 Vector Algebra 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 Vector Algebra 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 Vector Algebra. 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 Vector Algebra 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 Vector Algebra 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 Vector Algebra NCERT Chapter 10
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 Vector Algebra NCERT Chapter 10 useful.
Last but not least, to get the best hold on Class 12 Maths Vector Algebra NCERT Chapter 10, do not forget to check out:
- Vector Algebra Class 12 Maths Best videos
- Vector Algebra Class 12 Maths NCERT Solutions
- Class 12 Maths Vector Algebra Revision notes
- Vector Algebra Class 12 Maths DPPs, Download PDF of solutions
- Class 12 Maths Vector Algebra Online Tests
- Class 12 Maths Sample papers