by Tiwari Academy
NCERT Solutions for Class 12 Maths Chapter 10 Miscellaneous Exercise of Vector Algebra in Hindi and English Medium for academic session 2025-26. The questions and solutions of 12th Maths misc. ex. 10 are updated according to new NCERT textbook issued for CBSE 2025-26 exams.
12th Maths Chapter 10 Miscellaneous Exercise in Hindi and English
Class 12 Maths Chapter 10 Miscellaneous Exercise Solutions
Class XII Mathematics chapter 10 miscellaneous exercise solutions are updated for academic session 2025-26. Download solution in PDF file format or view online without downloading. Videos related to Miscellaneous Exercise 10 in Hindi and English Medium is also given free to use or download without any login or password.
| Class: 12 | Mathematics |
| Chapter: 10 | Miscellaneous Exercise 10 |
| Topic: | Vector Algebra |
| Content: | Textbook Exercise Solution |
| Content Type: | Text, PDF and Videos Format |
| Session: | Academic Year 2025-26 |
| Medium: | Hindi and English Medium |
NCERT Solutions for Class 12 Maths Miscellaneous Exercise 10
Download NCERT Solutions for Class 12 Maths Chapter 10 Miscellaneous Exercise 10 in PDF file format free to use. Hindi Medium and English Medium Solutions are available in PDF as well as video format free to use online or download.
Class 12 Maths Chapter 10 Miscellaneous Exercise 10 in Videos
Product of Two Vectors
In Mathematics 12, Chapter 10, we studied vector addition and subtraction. Another algebraic operation that we intend to discuss in relation to vectors is their product. Let us remember that the product of two numbers is a number, the product of two matrices is again a matrix. But in the case of functions, we can multiply them in two ways, namely the multiplication of two functions and the structure of two functions. Similarly, the Multiplication of two vectors is also defined in two ways, namely, the scalar product (or point) where the result is a scalar, and the vector (or cross) product where the result is a vector. Based on these two types of vector products, they have found various applications in geometry, mechanics, and engineering.
Vector (or cross) product of two vectors
Previously, we have discussed the right-hand three-dimensional rectangular coordinate system. In this system, when the positive x-axis is twisted counterclockwise towards the positive y-axis, a clockwise (standard) screw will move in the direction of the positive z-axis. In the right-handed coordinated system, the right-hand thumb points in the direction of the positive z-axis when the fingers curl away from the positive x-axis in the direction toward the positive y-axis.
History of Vectors
The word vector is derived from the Latin word vectus, meaning “carrying.” Germ ideas of modern vector theory date from around 1800 when Caspar Vessel (1745–1818) and Jean Robert Argund (1768–1822) described how a complex number a + ib could be given a geometric interpretation with the help of a directed line section in a coordinate plane. William Rowen Hamilton (1805–1865), an Irish mathematician, was the first to use the term vector for a directed line segment in his book Lectures on Quaternions (1853).
Which is the most important question of Miscellaneous Exercise 10 of 12th Maths?
Question number 12 and 14 are frequently asked in board exams, that is why these are considered as most important questions from miscellaneous 10.
Which example from miscellaneous 10 of 12th Maths is important for exams?
Example number 29 and 30 are tricky and important. Example 30 is asked so many times in CBSE board exams with variation of numbers.
