RD Sharma Class 12 Maths Solutions Chapter 25 - Vector or Cross Product

Consider a and b as two non-zero parallel vectors. The cross product of two vectors a and b is defined only in three-dimensional space and it is denoted by a×ba×b. The Vector is also known as Cross Product.

Vector Product is defined by the following formula:

$a \times b = \left | a \right | \left |b \right |\sin(\theta )n a \times b =  \left | a \right | \left |b \right |\sin(\theta )n$

Where |a||a| is the modulus of aa. It is also known as the magnitude of aa

$  \left |b \right | \left |b \right |$  is the modulus of bb

θθ is the angle between two vectors aa and bb, and nn is a unit vector

Following Are The Properties of Vector Product

1. Vector product does not follow the commutative rule. It is given by 

 $a \times b = -(b \times a)a\times b = -(b \times a)$

2. Vector multiplication rule

 $(ka) \times b = k(a \times b) = a \times(kb)(ka)\times b = k(a\times b) = a \times (kb)$

3. If the given vectors are collinear then a×b=0a×b=0

(Since the angle between both the vectors would be 00, then the value of $\sin(0)=0\sin(0)=0$)

4. a×ba×b in terms of unit vectors can be represented as

$a = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{j}a =  a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{j}$  

$b = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{j}b =  b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{j}$  

$a \times b = ( a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{j})( b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{j}) a \times b =  ( a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{j})( b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{j})$

5. Vector product follows distributive laws

 $a \times (b + c) = (a \times b) + (a \times c) a \times (b +c) = (a \times b)+(a \times c)$

Solutions For The Class12 Rd Sharma Maths Chapter 25 Vector Or Cross Product Is Available For A Free Download In A PDF File Format

Chapter 25th of the Class 12 RD Sharma Math book is Vector or Cross Product. And to ace in this Chapter students require a good amount of practice in solving the questions from this Chapter. Because the more practice of the Chapter 25 Vector or Cross Product a student does the better, they become. Solving the questions develops the various skills in the students helpful for the final Class 12 exam, such as it decreases the time taken for solving a single question, also it helps in increasing the accuracy of solving the question. And these two skills are the most important ones for the exam.

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Also, if you are looking for the solutions of the next Chapter which is Scalar Triple Product you can find it here: RD Sharma Class 12 Math Solutions Chapter 26 - Scalar Triple Product ()

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