NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra covers important concepts of the difference between a scalar and a vector quantity, the properties of these quantities, and the operations of vectors. There are two types of physical quantities, scalars and vectors. The scalar quantity has only magnitude, whereas the vector quantity has both magnitude and direction. Vector algebra studies the algebra of vector quantities.

The chapters Vectors and Three Dimensional Geometry holds a weightage of 14 marks in the CBSE Class 12 Examination. The questions asked in the examination test the concepts of types of vectors (equal, zero, unit, parallel and collinear vectors), position vector, negative of a vector, addition of vectors, multiplication of a vector by a scalar, and vector (cross) product of vectors.

Download PDF: NCERT Solutions for Class 12 Mathematics Chapter 10

NCERT Solutions for Class 12 Mathematics Chapter 10 Vector Algebra

Important Topics in Class 12 Mathematics Chapter 10 Vector Algebra

A vector has both magnitudes and direction. It is represented by an arrow that shows the direction (→) and its length shows the magnitude.

The vector is denoted as \(\overrightarrow V\)and its magnitude is represented as \|V\|.

Addition of Vectors: Let us consider there are two vectors P and Q, then the sum of these vectors can be when the tail of vector Q meets the head of vector A. During this addition, the magnitude and direction of the vectors should not change.

The vector addition follows these important laws: Commutative Law: P + Q = Q + P Associative Law: P + (Q + R) = (P + Q) + R

Subtraction of Vectors: In the subtraction of vectors, the direction of one vector is reversed and then the addition is performed on both the vectors.

It can be denoted as P – Q = P + (-Q)

Multiplication of Vectors: If k is a scalar quantity and is multiplied by vector A, then scalar multiplication is given by kA.

If k is positive then the direction of the vector kA is the direction of vector A, but if the value of k is negative, then the direction of vector kA is opposite of the direction of vector A. The magnitude of the vector kA can be calculated by \|kA\|.

Dot Product: The dot product is a scalar product. It is represented using a dot (.) between the two vectors.

Suppose P and Q are two given vectors, then the dot product for both the vectors is given through P.Q = \|P\| \|Q\| cosθ.

Cross Product: Denoted by a multiplication sign (x) between two vectors, the cross product is a binary vector operation that is defined in a three-dimensional system.

It is represented as P x Q = \|P\| \|Q\| sinθ

NCERT Solutions For Class 12 Maths Chapter 10 Exercises

The detailed solutions for all the NCERT Solutions for Chapter 10 Vector Algebra in different exercises are as follows:

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CBSE CLASS XII Related Questions

1.
Find the value of λ, if the points A(−1,−1,2), B(2,8,λ), C(3,11,6) are collinear.

View Solution

2.
Find : \[ I = \int \frac{x + \sin x}{1 + \cos x} \, dx \]

View Solution

3.
The domain of the function \( f(x) = \cos^{-1}(2x) \) is:

\([-1, 1]\)
\(\left[0, \frac{1}{2}\right]\)
\([-2, 2]\)
\(\left[-\frac{1}{2}, \frac{1}{2}\right]\)

View Solution

4.
Let \( \vec{a} \) and \( \vec{b} \) be two co-initial vectors forming adjacent sides of a parallelogram such that:
\[ |\vec{a}| = 10, \quad |\vec{b}| = 2, \quad \vec{a} \cdot \vec{b} = 12 \] Find the area of the parallelogram.

View Solution

5.
If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]

View Solution

6.
An amount of ₹ 10,000 is put into three investments at the rate of 10%, 12% and 15% per annum. The combined annual income of all three investments is ₹ 1,310, however, the combined annual income of the first and second investments is ₹ 190 short of the income from the third. Use matrix method and find the investment amount in each at the beginning of the year.

View Solution

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

NCERT Solutions for Class 12 Mathematics Chapter 10 Vector Algebra

Important Topics in Class 12 Mathematics Chapter 10 Vector Algebra

NCERT Solutions For Class 12 Maths Chapter 10 Exercises

CBSE CLASS XII Related Questions

1.
Find the value of λ, if the points A(−1,−1,2), B(2,8,λ), C(3,11,6) are collinear.

2.
Find : \[ I = \int \frac{x + \sin x}{1 + \cos x} \, dx \]

3.
The domain of the function \( f(x) = \cos^{-1}(2x) \) is:

4.
Let \( \vec{a} \) and \( \vec{b} \) be two co-initial vectors forming adjacent sides of a parallelogram such that:
\[ |\vec{a}| = 10, \quad |\vec{b}| = 2, \quad \vec{a} \cdot \vec{b} = 12 \] Find the area of the parallelogram.

5.
If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]

Similar Mathematics Concepts

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NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

NCERT Solutions for Class 12 Mathematics Chapter 10 Vector Algebra

Important Topics in Class 12 Mathematics Chapter 10 Vector Algebra

NCERT Solutions For Class 12 Maths Chapter 10 Exercises

CBSE CLASS XII Related Questions

1.Find the value of λ, if the points A(−1,−1,2), B(2,8,λ), C(3,11,6) are collinear.

2. Find : \[ I = \int \frac{x + \sin x}{1 + \cos x} \, dx \]

3.The domain of the function \( f(x) = \cos^{-1}(2x) \) is:

4. Let \( \vec{a} \) and \( \vec{b} \) be two co-initial vectors forming adjacent sides of a parallelogram such that: \[ |\vec{a}| = 10, \quad |\vec{b}| = 2, \quad \vec{a} \cdot \vec{b} = 12 \] Find the area of the parallelogram.

5.If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Find the value of λ, if the points A(−1,−1,2), B(2,8,λ), C(3,11,6) are collinear.

2.
Find : \[ I = \int \frac{x + \sin x}{1 + \cos x} \, dx \]

3.
The domain of the function \( f(x) = \cos^{-1}(2x) \) is:

4.
Let \( \vec{a} \) and \( \vec{b} \) be two co-initial vectors forming adjacent sides of a parallelogram such that:
\[ |\vec{a}| = 10, \quad |\vec{b}| = 2, \quad \vec{a} \cdot \vec{b} = 12 \] Find the area of the parallelogram.

5.
If \( \mathbf{a} \) and \( \mathbf{b} \) are position vectors of two points \( P \) and \( Q \) respectively, then find the position vector of a point \( R \) in \( QP \) produced such that \[ QR = \frac{3}{2} QP. \]