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NCERT Solutions for Exercise 10.3 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 10.3 Class 12 Maths chapter 10 explains the questions related to dot products of vectors. As far as the unit vector algebra is concerned dot product is an important topic. NCERT syllabus Exercise 10.3 Class 12 Math familiarise the students with the concept of dot products. NCERT solutions for Class 12 Maths chapter 10 exercise 10.3 are framed by maths expert and is in accordance with the CBSE syllabus. Students can use Class 12 Maths chapter 10 exercise 10.3 for the preparations of CBSE Class 12 Board Exams. Along with NCERT practice CBSE Previous Year Class 12 Maths Questions to get a good score in board exam.
12th class Maths exercise 10.3 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.
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Question:1 Find the angle between two vectors with magnitudes , respectively having .
Answer:
Given
As we know
where is the angle between two vectors
So,
Hence the angle between the vectors is .
Question:2 Find the angle between the vectors
Answer:
Given two vectors
Now As we know,
The angle between two vectors and is given by
Hence the angle between
Question:3 Find the projection of the vector on the vector
Answer:
Let
Projection of vector on
Hence, Projection of vector on is 0.
Question:4 Find the projection of the vector on the vector
Answer:
Let
The projection of on is
Hence, projection of vector on is
Answer:
Given
Now magnitude of
Hence, they all are unit vectors.
Now,
Hence all three are mutually perpendicular to each other.
Answer:
Given two vectors
Now Angle between
Now As we know that
Hence, the magnitude of two vectors
Question:9 Find , if for a unit vector
Answer:
Given in the question that
And we need to find
So the value of is
Question:10 If are such that is perpendicular to , then find the value of
Answer:
Given in the question is
and is perpendicular to
and we need to find the value of ,
so the value of -
As is perpendicular to
the value of ,
Question:11 Show that is perpendicular to , for any two nonzero vectors .
Answer:
Given in the question that -
are two non-zero vectors
According to the question
Hence is perpendicular to .
Question:12 If , then what can be concluded about the vector ?
Answer:
Given in the question
Therefore is a zero vector. Hence any vector will satisfy
Question:13 If are unit vectors such that , find the value of
Answer:
Given in the question
are unit vectors
and
and we need to find the value of
Answer- the value of is
Question:14 If either vector . But the converse need not be true. Justify your answer with an example
Answer:
Let
we see that
we now observe that
Hence here converse of the given statement is not true.
Answer:
Given points,
A=(1, 2, 3),
B=(–1, 0, 0),
C=(0, 1, 2),
As need to find Angle between
Hence angle between them ;
Answer - Angle between the vectors is
Question:16 Show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear.
Answer:
Given in the question
A=(1, 2, 7), B=(2, 6, 3) and C(3, 10, –1)
To show that the points A(1, 2, 7), B(2, 6, 3) and C(3, 10, –1) are collinear
As we see that
Hence point A, B , and C are colinear.
Question:17 Show that the vectors form the vertices of a right angled triangle.
Answer:
Given the position vector of A, B , and C are
To show that the vectors form the vertices of a right angled triangle
Here we see that
Hence A,B, and C are the vertices of a right angle triangle.
Question:18 If is a nonzero vector of magnitude ‘a’ and a nonzero scalar, then is unit vector if
Answer:
Given is a nonzero vector of magnitude ‘a’ and a nonzero scalar
is a unit vector when
Hence the correct option is D.
There are a total of 18 questions from exercise 10.3 Class 12 Maths. These questions mainly are based on the concepts of dot products. Dot products are used to identify orthogonal vectors and the projections of a vector. Question number 4 of Class 12 Maths chapter 10 exercise 10.3 gives an example of the projection of a vector on another.
Also Read | Vector Algebra Class 10 Chapter 10 Notes
Yes. For two perpendicular vectors, the dot product is zero.
The main three topics are the addition of vectors, the dot product of vectors and the cross product of vectors.
The work done is the dot product of force and displacement. The dot product of two vectors is a scalar (real number).
The dot product of force and velocity gives power.
i.k=0 as the angle between them is 90 degrees
Yes, the dot product of two vectors can be either positive, negative or zero based on the angle between them.
There are a total of 5 exercises including miscellaneous.
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