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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-
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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.
You can use them people also used problem
Hi,
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The scholarships are categorized based on the marks obtained in the exam: Type A for those scoring 60% or above, Type B for scores between 50% and 60%, and Type C for scores between 40% and 50%. The cash scholarships range from Rs. 2,000 to Rs. 18,000 per month, depending on the exam and the marks obtained.
Since you already have a 12th-grade qualification with 84%, you meet the eligibility criteria and can apply for the Medhavi Scholarship exam. Preparing well for the exam can increase your chances of receiving a higher scholarship.
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.
Hello student,
If you are planning to appear again for class 12th board exam with PCMB as a private candidate here is the right information you need:
Remember
, these are tentative dates based on last year. Keep an eye on the CBSE website ( https://www.cbse.gov.in/ ) for the accurate and official announcement.
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 help you.
Good luck with your studies!
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