NCERT Solutions for Class 12 Maths Chapter 10 Exercise 10.4 Vector Algebra - PDF Download

1. Vector (or cross) product of two vectors

When the positive x-axis is rotated counterclockwise into the positive y-axis, a right handed (standard) screw would advance in the direction of the positive z-axis. 

In a right handed coordinate system, the thumb of the right hand points in the direction of the positive z-axis when the fingers are curled in the direction away from the positive x-axis toward the positive y-axis. 

The vector product of two nonzero vectors $\vec{a}$ and $\vec{b}$,  is denoted by $\vec{a} \times \vec{b}$ and defined as

                                   $\vec{a} \times \vec{b}=|\vec{a} \| \vec{b}| \sin \theta \hat{n}$

where, θ is the angle between $\vec{a}$ and $\vec{b}$ , 0 ≤ θ ≤ π and \hat{n} is a unit vector perpendicular to both $\vec{a}$ and $\vec{b}$ such $\vec{a}, \vec{b}$ and $\hat{n}$ that form a right handed system.

Property 3 (Distributivity of vector product over addition): If $\vec{a}, \vec{b}$ and $\vec{c}$ are any three vectors and λ be a scalar, then 

1. $\vec{a} \times(\vec{b}+\vec{c})=\vec{a} \times \vec{b}+\vec{a} \times \vec{c}$

2. $\lambda(\vec{a} \times \vec{b})=(\lambda \vec{a}) \times \vec{b}=\vec{a} \times(\lambda \vec{b})$

          Let $\vec{a}$ and $\vec{b}$ be two vectors given in component form as $a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}$ and $b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$ , respectively. Then their cross product may be given by 

                         $\vec{a} \times \vec{b}=\left|\begin{array}{ccc}\hat{i} & \hat{j} & \hat{k} \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3\end{array}\right|$

Tips for Solving Exercise 10.4 Class 12 Chapter 10 Differential Equations

In class 12 maths chapter 10 exercise 10.4 NCERT solutions, our academic team of mathematics have provided some of the useful tips for solving questions of exercise 10.4 class 12 maths chapter 10.

1. Students must practice NCERT solutions for class 12 maths chapter 10 ex 10.4 as the concepts mentioned in this exercise are a little bit tricky.

2. You must remember the formula and property of cross product of two vectors for gaining a deep knowledge of the topic.

3. This exercise also talks about the property of the distributivity of vector product over addition which is an important aspect for ex 10.4. You should go through this concept for easy solutions of questions asked in ex 10.4 class 12 maths chapter 10.
   

Importance of Solving Ex 10.4 Class 12 Maths Chapter 10 Differential Equations

There are several benefits of solving ex 10.4 class 12 maths chapter 10 Differential Equations. You can check some of them provided by eSaral’s expert teachers for clear comprehension of questions.

1. In NCERT solutions for class 12 maths chapter 10 ex 10.4, subject experts of eSaral have explained all the concepts in precise and simple language for students to solve each question without any doubt.

2. NCERT solutions are provided in PDF format so that you can cross check your answers.

3. Practicing questions and revising concepts from NCERT solutions will help you to score high marks in board exams.

4. There are a lot of examples related to concepts mentioned in ex 10.4. You must practice these examples for better understanding of questions.
   

Frequently Asked Questions

Question 1. Write the formula for the cross product of two vectors?

Answer 1. The formula for finding the cross product of two vectors is as follows.

If θ is the angle between two vectors $\vec{a}$ and $\vec{b}$ , then their cross product is given as 

            $\vec{a} \times \vec{b}=|\vec{a}||\vec{b}| \sin \theta \hat{n}$

Question 2. What is the main concept of ex 10.4 class 12 maths chapter 10?

Answer 2. The main concept of ex 10.4 class 12 maths chapter 10 is the vector (or cross) product of two vectors. You will be learning the concept where a third vector is perpendicular to the two original ones. By the rule of right-hand thumb, you will be able to calculate the magnitude by measuring the area of the parallelogram between them.