RD Sharma Class 12 Chapter 25 Solutions (Vector Or Cross Product)
RD Sharma Class 12 Maths Solutions Chapter 25 Vector or Cross Product tests your knowledge on cross-product vectors. RD Sharma Solutions is based on the topics of the chapter such as vector (or Cross) product, six properties of vector product, geometrical interpretation of vector product, vector product in terms of components, vectors normal to the plane of two vectors, some important results, Lagrange’s identity, vector product of given vectors, on finding a unit vector and a vector of given magnitude perpendicular to two given vectors, on finding the area of the parallelogram, on finding the area of a quadrilateral, on finding the area of a triangle, etc.
Chapter 25 ‘Vector or Cross Products’ contains one exercise and 34 questions where you will answer all on the basis of the topics discussed. The pattern and type of questions you solve here are very similar to what you will find in CBSE as well as competitive exams like JEE Main or JEE Advanced.
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Topics Discussed in RD Sharma Class 12 Maths Solutions Chapter 25 – Vector or Cross Product
Vector (or Cross) Product
Let the two vectors, a and b are the non-parallel and non-zero vectors. Then the product of the two vectors (a vector x b vector) in that particular order can be defined as a vector with magnitude |a vector||b vector|sinø where ø is necessarily the angle between the two vectors.
The direction of ø can be found as perpendicular to the plane of the two given vectors in such a way the two vectors and this direction together form a right-handed system.
Note 1 – If one of the two vectors, vector a of vector b or both are zero vector, then ø cannot be defined as 0 vectors. Ø will not be defined. And the direction ƒ will also not be defined.
Note 2 – If the two vectors are collinear i.e. if ø = 0 or, then the direction ƒ will not be well defined. In such a case, the cross of the two vectors is equal to zero.
Note 3 – vector a x vector b is known as vector a cross vector b. As we insert a cross between the two vectors, we call it a cross-product. As a result, the cross-product of the two vectors is a vector product.
Note 4 – Vector area of a plane means that a magnitude of the vector will be equal to the area of that figure and its direction which is found normal to the plane in the right-handed direction.
Properties of a vector product
- Vector product can never be commutative i.e. cross product of two vectors, i.e. (vector a x vector b) = – (vector b x vector a).
- Consider the two vectors, vector a and vector b and m a scalar
Then, m vector a x vector b = m(vector a x vector b) = vector a x m vector b
- The two vectors, vector a and vector b and m, n are scalars,
Then m vector a x n vector b = mn(vector a x vector b) = m(vector a x n vector b) = n(m vector a x vector b).
Discussion of Exercises in RD Sharma Class 12 Maths Solutions Chapter 25 Vector or Cross Product
The RD Sharma Class 12 Maths Solutions Chapter 25 Vector or Cross Product discusses more finding the cross product of the two vectors given the values of these vectors, finding the magnitude of the two given vectors, finding the area of parallelogram where diagonals are given, finding the angle between the two vectors, verifying two given vectors are perpendicular to each other, finding the area of the triangle, finding the unit vector perpendicular to the given vectors, etc.
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