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Exercise 10.2 of Class 12 Maths Chapter 10 helps you understand how to add vectors, find their magnitude, and break them into components, just like combining forces or directions in real life. For example, pilots and sailors use vector addition to navigate through air or water currents. NCERT solution for Class 12 is highly beneficial for Class 12 board exams, along with competitive exams such as JEE Main and others.
Class 12 maths chapter 10 exercise 10.2 solutions is not only beneficial in maths, it has a major contribution to physics also, particularly in topics such as motion, forces and electric field. These NCERT exercise solutions are made by expert faculty with clear, step-by-step methods to make tough problems easier. Practising these builds strong concepts and boosts your confidence for both board exams and competitive exams.
No, the Central Board of Secondary Education is yet to declare CBSE Class 10 results 2025. Once declared, the CBSE 10th result link 2025 will be available on the official website, results.cbse.nic.in.
Access NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.2 to strengthen your understanding of vector operations like addition, scalar multiplication, and components of vectors. These step-by-step NCERT solutions are perfect for the final exam and homework help.
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
Answer:
Hence when,
Question 5: Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (– 5, 7).
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,
Answer:
Given
Now,
Now a unit vector in the direction of
Question 10: Find a vector in the direction of vector
Answer:
Given a vector
the unit vector in the direction of
A vector in direction of
Question 11: Show that the vectors
Answer:
Let
It can be seen that
Hence here
As we know
Whenever we have
Here
Hence vectors
Question 13: Find the direction cosines of the vector joining the points A(1, 2, –3) and B(–1, –2, 1), directed from A to B.
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
Answer:
Let
Hence direction cosines of this vectors is
Let
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:
Question 17: Show that the points A, B and C with position vectors,
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:
(A) If two vectors are collinear then, they have the same direction or are parallel or antiparallel.Therefore, They can be expressed in the form
(B)
(C) The vectors
(D) The vectors
Addition of Vectors:
A vector
This is known as the triangle law of vector addition.
Multiplication of a Vector by a Scalar:
Let
Also Read
Also see-
As per latest 2024 syllabus. Maths formulas, equations, & theorems of class 11 & 12th chapters
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.
Admit Card Date:17 April,2025 - 17 May,2025
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Changing from the CBSE board to the Odisha CHSE in Class 12 is generally difficult and often not ideal due to differences in syllabi and examination structures. Most boards, including Odisha CHSE , do not recommend switching in the final year of schooling. It is crucial to consult both CBSE and Odisha CHSE authorities for specific policies, but making such a change earlier is advisable to prevent academic complications.
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!
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As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters
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