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NCERT Solutions for Exercise 10.2 Class 12 Maths Chapter 10 Vector Algebra are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. NCERT solutions for exercise 10.2 Class 12 Maths chapter 10 introduces a few more concepts of vectors. The questions of exercise 10.2 Class 12 Maths deals with the concepts like addition of vectors, magnitude of vectors, unit vectors etc. Also in NCERT solutions for Class 12 Maths chapter 10 exercise 10.2 questions related to collinear vectors and components of vectors. As the Class 12 Maths syllabus is concerned, it is important to practice Class 12 Maths chapter 10 exercise 10.2. Questions related to the Class 12th Maths chapter 10 exercise 10.2 can be expected for CBSE Class 12 Board Exams as well as competitive exams like JEE Mains.
The chapter Vector Algebra exercises will be helpful for both Mathematics and Physics. To solve more problems of NCERT Class 12 Maths, students can also make use of NCERT Exemplar Solutions for Class 12 Maths. 12th class Maths exercise 10.2 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.
Also practice-
Question:1 Compute the magnitude of the following vectors:
(1)
Answer:
Here
Magnitude of
Question:2 Write two different vectors having same magnitude
Answer:
Two different Vectors having the same magnitude are
The magnitude of both vector
Question:3 Write two different vectors having same direction.
Answer:
Two different vectors having the same direction are:
Question:4 Find the values of x and y so that the vectors and are equal.
Answer:
will be equal to when their corresponding components are equal.
Hence when,
and
Answer:
Let point P = (2, 1) and Q = (– 5, 7).
Now,
Hence scalar components are (-7,6) and the vector is
Question:7 Find the unit vector in the direction of the vector
Answer:
Given
Magnitude of
A unit vector in the direction of
Answer:
Given P = (1, 2, 3) and Q = (4, 5, 6)
A vector in direction of PQ
Magnitude of PQ
Now, unit vector in direction of PQ
Question:9 For given vectors, and , find the unit vector in the direction of the vector .
Answer:
Given
Now,
Now a unit vector in the direction of
Question:10 Find a vector in the direction of vector which has magnitude 8 units.
Answer:
Given a vector
the unit vector in the direction of
A vector in direction of and whose magnitude is 8 =
Question:11 Show that the vectors and are collinear.
Answer:
Let
It can be seen that
Hence here
As we know
Whenever we have , the vector and will be colinear.
Here
Hence vectors and are collinear.
Answer:
Given
point A=(1, 2, –3)
point B=(–1, –2, 1)
Vector joining A and B Directed from A to B
Hence Direction cosines of vector AB are
Question:14 Show that the vector is equally inclined to the axes OX, OY and OZ.
Answer:
Let
Hence direction cosines of this vectors is
Let , and be the angle made by x-axis, y-axis and z- axis respectively
Now as we know,
,
Hence Given vector is equally inclined to axis OX,OY and OZ.
Answer:
As we know
The position vector of the point R which divides the line segment PQ in ratio m:n internally:
Here
position vector os P = =
the position vector of Q =
m:n = 2:1
And Hence
Answer:
As we know
The position vector of the point R which divides the line segment PQ in ratio m:n externally:
Here
position vector os P = =
the position vector of Q =
m:n = 2:1
And Hence
Question:16 Find the position vector of the mid point of the vector joining the points P(2, 3, 4) and Q(4, 1, –2).
Answer:
Given
The position vector of point P =
Position Vector of point Q =
The position vector of R which divides PQ in half is given by:
Answer:
Given
the position vector of A, B, and C are
Now,
AS we can see
Hence ABC is a right angle triangle.
Question:18 In triangle ABC (Fig 10.18), which of the following is not true:
Answer:
From triangles law of addition we have,
From here
also
Also
Hence options A,B and D are true SO,
Option C is False.
Answer:
If two vectors are collinear then, they have same direction or are parallel or anti-parallel.
Therefore,
They can be expressed in the form where a and b are vectors and is some scalar quantity.
Therefore, (a) is true.
Now,
(b) is a scalar quantity so its value may be equal to
Therefore,
(b) is also true.
C) The vectors and are proportional,
Therefore, (c) is not true.
D) The vectors and can have different magnitude as well as different directions.
Therefore, (d) is not true.
Therefore, the correct options are (C) and (D).
The NCERT Class 12 Math chapter 10 exercise 10.2 starts with the questions to find the magnitude of vectors. The 5th question of exercise 10.2 Class 12 Maths is related to the concept of position vector. The concepts of unit vectors are explained in questions 7 to 10. NCERT solutions for Class 12 Maths chapter 10 exercise 10.2 also goes through the topics like direction cosines, and section formula.
Also Read | Vector Algebra Class 10 Chapter 10 Notes
Yes, two different vectors can have the same magnitude. These vectors may be pointing in a different direction. An example is shown in question number 2 of NCERT solutions for Class 12 Maths chapter 10 exercise 10.2.
Yes, two different vectors can have the same direction. It can be vectors with different magnitudes. The third question of exercise 10.2 Class 12 Maths gives an example of this.
The question may be to find a unit vector in the direction of a given vector, or it may be related to collinear vectors etc.
There are a total of 19 questions. Practising these may help in the CBSE Class 12 Maths Paper
The concepts in Vector Algebra help to solve NEET physics problems. A good part of Class 11 and Class 12 NCERT Physics Syllabus uses the concepts of vectors. So vectors will be useful for the NEET exam as well as for engineering entrance exams like JEE Main.
The given vectors are equal. Which implies that 2x=7. Therefore x=3.5. And 3y=6, therefore y=2
One method to solve such kinds of problems is to find the magnitudes of given vectors and verify Pythagoras Theorem.
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Hello there! Thanks for reaching out to us at Careers360.
Ah, you're looking for CBSE quarterly question papers for mathematics, right? Those can be super helpful for exam prep.
Unfortunately, CBSE doesn't officially release quarterly papers - they mainly put out sample papers and previous years' board exam papers. But don't worry, there are still some good options to help you practice!
Have you checked out the CBSE sample papers on their official website? Those are usually pretty close to the actual exam format. You could also look into previous years' board exam papers - they're great for getting a feel for the types of questions that might come up.
If you're after more practice material, some textbook publishers release their own mock papers which can be useful too.
Let me know if you need any other tips for your math prep. Good luck with your studies!
It's understandable to feel disheartened after facing a compartment exam, especially when you've invested significant effort. However, it's important to remember that setbacks are a part of life, and they can be opportunities for growth.
Possible steps:
Re-evaluate Your Study Strategies:
Consider Professional Help:
Explore Alternative Options:
Focus on NEET 2025 Preparation:
Seek Support:
Remember: This is a temporary setback. With the right approach and perseverance, you can overcome this challenge and achieve your goals.
I hope this information helps you.
Hi,
Qualifications:
Age: As of the last registration date, you must be between the ages of 16 and 40.
Qualification: You must have graduated from an accredited board or at least passed the tenth grade. Higher qualifications are also accepted, such as a diploma, postgraduate degree, graduation, or 11th or 12th grade.
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Get Scholarship: Following a successful verification process, the scholarship will be given. You need to have at least passed the 10th grade/matriculation scholarship amount will be transferred directly to your bank account.
Scholarship Details:
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Type B: For candidates scoring between 50% and 60%.
Type C: For candidates scoring between 40% and 50%.
Cash Scholarship:
Scholarships can range from Rs. 2,000 to Rs. 18,000 per month, depending on the marks obtained and the type of scholarship exam (SAKSHAM, SWABHIMAN, SAMADHAN, etc.).
Since you already have a 12th grade qualification with 84%, you meet the qualification criteria and are eligible to apply for the Medhavi Scholarship exam. Make sure to prepare well for the exam to maximize your chances of receiving a higher scholarship.
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hello mahima,
If you have uploaded screenshot of your 12th board result taken from CBSE official website,there won,t be a problem with that.If the screenshot that you have uploaded is clear and legible. It should display your name, roll number, marks obtained, and any other relevant details in a readable forma.ALSO, the screenshot clearly show it is from the official CBSE results portal.
hope this helps.
Hello Akash,
If you are looking for important questions of class 12th then I would like to suggest you to go with previous year questions of that particular board. You can go with last 5-10 years of PYQs so and after going through all the questions you will have a clear idea about the type and level of questions that are being asked and it will help you to boost your class 12th board preparation.
You can get the Previous Year Questions (PYQs) on the official website of the respective board.
I hope this answer helps you. If you have more queries then feel free to share your questions with us we will be happy to assist you.
Thank you and wishing you all the best for your bright future.
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