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Curious to know how well you have learned Vector Algebra? The NCERT Solutions for Class 12 maths chapter 10 miscellaneous exercise are ideal to test your knowledge with mixed and challenging questions. These 19 questions cover all that you have learned till now in this chapter, and help you revise and increase your confidence level before exams. These solutions are prepared by Careers360 experts, these solutions are according to the latest CBSE syllabus.
Attempt to solve the Class 12 Maths Chapter 10 Miscellaneous Exercise of NCERT yourself to gauge how well you have understood the concepts. These questions are a combination of all important topics and assist you in analyzing what needs to be revised. The NCERT solution for Class 12 Maths are aimed at building your foundation through step-by-step solutions.
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Question 1: Write down a unit vector in XY-plane, making an angle of
Answer:
As we know
a unit vector in XY-Plane making an angle
Hence for
Answer- the unit vector in XY-plane, making an angle of
Question 2: Find the scalar components and magnitude of the vector joining the points
Answer:
Given in the question
And we need to finrd the scalar components and magnitude of the vector joining the points P and Q
Magnitiude of vector PQ
Scalar components are
Answer:
As the girl walks 4km towards west
Position vector =
Now as she moves 3km in direction 30 degree east of north.
hence final position vector is;
Question 4: If
Answer:
No, if
the condition
also, in a triangle,
Since, the condition
Question 5: Find the value of x for which
Answer:
Given in the question,
a unit vector,
We need to find the value of x
The value of x is
Question 6: Find a vector of magnitude 5 units, and parallel to the resultant of the vectors
Answer:
Given two vectors
Resultant of
Now, a unit vector in the direction of
Now, a unit vector of magnitude in direction of
Hence the required vector is
Question 7: If
Answer:
Given in the question,
Now,
let vector
Now, a unit vector in direction of
Now,
A unit vector parallel to
OR
Answer:
Given in the question,
points A(1, – 2, – 8), B(5, 0, –2) and C(11, 3, 7)
now let's calculate the magnitude of the vectors
As we see that AB = BC + AC, we conclude that three points are colinear.
we can also see from here,
Point B divides AC in the ratio 2 : 3.
Answer:
Given, two vectors
the point R which divides line segment PQ in ratio 1:2 is given by
Hence position vector of R is
Now, Position vector of the midpoint of RQ
which is the position vector of Point P . Hence, P is the mid-point of RQ
Question 10: The two adjacent sides of a parallelogram are
Answer:
Given, two adjacent sides of the parallelogram
The diagonal will be the resultant of these two vectors. so
resultant R:
Now unit vector in direction of R
Hence unit vector along the diagonal of the parallelogram
Now,
Area of parallelogram
Hence the area of the parallelogram is
Question 11: Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are
Answer:
Let a vector
let direction cosines of this vector be
Now
Hence direction cosines are:
Question 12: Let
Answer:
Given,
Let
now, since it is given that d is perpendicular to
And
here we got 2 equation and 3 variable. one more equation will come from the condition:
so now we have three equations and three variables,
On solving this three equation we get,
Hence required vector :
Question 13: The scalar product of the vector
Answer:
Let, the sum of vectors
unit vector along
Now, the scalar product of this with
Question 14: If
Answer:
Given
Now, let vector
Now,
Now, Since,
Hence vector
Question 15: Prove that
Answer:
Given in the question,
= RHS
LHS ie equal to RHS
Hence proved.
Question 16: Choose the correct answer If
Answer:
Given in the question
this will satisfy when
Hence option B is the correct answer.
Question 18: The value of
(A) 0
(B) –1
(C) 1
(D) 3
Answer:
To find the value of
Hence option C is correct.
Question 19: Choose the correct. If
is equal to
(A) 0
(B)
( C )
( D )
Answer:
Given in the question
To find the value of
Hence, option D is correct.
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Frequently Asked Questions (FAQs)
Vectors is an important chapter of Class 12 Maths NCERT syllabus. The concepts studied in this chapter are used not only on mathematics but also to solve problems in Class 11 and 12 physics problems also. Also Vectors is an important chapter for CBSE Board exam. Solving the NCERT questions and referring to the NCERT exemplar will be beneficial for board exam preparation.
The topics covered are vectors basic concepts, algebra of vectors, direction cosine and ratios, dot product and cross product of vectors.
On Question asked by student community
Hello
Yes, if you’re not satisfied with your marks even after the improvement exam, many education boards allow you to reappear as a private candidate next year to improve your scores. This means you can register independently, study at your own pace, and take the exams without attending regular classes. It’s a good option to improve your results and open up more opportunities for higher studies or careers. Just make sure to check the specific rules and deadlines of your education board so you don’t miss the registration window. Keep your focus, and you will do better next time.
Hello Aspirant,
Yes, in the case that you appeared for the 2025 improvement exam and your roll number is different from what was on the previous year’s marksheet, the board will usually release a new migration certificate. This is because the migration certificate will reflect the most recent exam details, roll number and passing year. You can apply to get it from your board using the process prescribed by them either online or through your school/college.
Yes, if you miss the 1st CBSE exam due to valid reasons, then you can appear for the 2nd CBSE compartment exam.
From the academic year 2026, the board will conduct the CBSE 10th exam twice a year, while the CBSE 12th exam will be held once, as per usual. For class 10th, the second phase exam will act as the supplementary exam. Check out information on w hen the CBSE first exam 2026 will be conducted and changes in 2026 CBSE Board exam by clicking on the link .
If you want to change your stream to humanities after getting a compartment in one subject in the CBSE 12th Board Exam , you actually have limited options to qualify for your board exams. You can prepare effectively and appear in the compartment examination for mathematics again. If you do not wish to continue with the current stream, you can take readmission in the Humanities stream and start from Class 11th again, and continue studying for two more years to qualify for the 12th examination.
The GUJCET Merit List is prepared based on the Class 12th marks and GUJCET marks received by the students. CBSE students who are not from the Gujarat board can definitely compete with GSEB students, as their eligibility is decided based on the combined marks scored by them in GUJCET and the 12th board. The weightage of the GUJCET score is 40% and the weightage of the class 12 scores is 60%.
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