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.
Smoking increases the risk of lung problems. A study revealed that 170 in 1000 males who smoke develop lung complications, while 120 out of 1000 females who smoke develop lung related problems. In a colony, 50 people were found to be smokers of which 30 are males. A person is selected at random from these 50 people and tested for lung related problems. Based on the given information answer the following questions:

(i) What is the probability that selected person is a female?
(ii) If a male person is selected, what is the probability that he will not be suffering from lung problems?
(iii)(a) A person selected at random is detected with lung complications. Find the probability that selected person is a female.
OR
(iii)(b) A person selected at random is not having lung problems. Find the probability that the person is a male.

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2.
The probability of hitting the target by a trained sniper is three times the probability of not hitting the target on a stormy day due to high wind speed. The sniper fired two shots on the target on a stormy day when wind speed was very high. Find the probability that
(i) target is hit.
(ii) at least one shot misses the target.

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3.
A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.

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4.
If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
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5.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

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Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

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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

5.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

6.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

Similar Mathematics Concepts

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dOGVmW

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

5.A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

6.Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]

Similar Mathematics Concepts

Comments

dOGVmW

5.
A rectangle of perimeter \(24\) cm is revolved along one of its sides to sweep out a cylinder of maximum volume. Find the dimensions of the rectangle.

6.
Find : \[ \int \frac{2x+1}{\sqrt{x^2+6x}}\,dx \]