Properties of Cross Product

# Properties of Cross Product Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

205 videos|264 docs|139 tests

## FAQs on Properties of Cross Product Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What is the definition of cross product in mathematics?
Ans. The cross product is a binary operation on two vectors in a three-dimensional space that results in a vector perpendicular to both of the original vectors. It is also known as the vector product.
 2. How is the cross product calculated between two vectors?
Ans. The cross product between two vectors, let's say A and B, is calculated using the determinant of a 3x3 matrix. The resulting vector is given by: A x B = (A2B3 - A3B2) i + (A3B1 - A1B3) j + (A1B2 - A2B1) k Here, i, j, and k are the unit vectors along the x, y, and z axes, respectively.
 3. What is the geometric interpretation of the cross product?
Ans. Geometrically, the cross product of two vectors represents a vector that is perpendicular to both of the original vectors. Its magnitude is equal to the area of the parallelogram formed by the two vectors, and its direction follows the right-hand rule.
 4. Is the cross product commutative?
Ans. No, the cross product is not commutative. In other words, A x B is not equal to B x A. The order of the vectors matters, and the resulting vector will have opposite directions when the order is reversed.
 5. What are some applications of the cross product in physics and engineering?
Ans. The cross product is widely used in physics and engineering. It is used to calculate torque, determine the direction of magnetic fields, analyze fluid flow, and solve problems in mechanics, electromagnetism, and computer graphics, among others.

## Mathematics (Maths) Class 12

205 videos|264 docs|139 tests

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