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Overview of Scalar and Vector Product of 2 Vectors Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Overview of Scalar and Vector Product of 2 Vectors Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is the scalar product of two vectors?
The scalar product, also known as the dot product, is a mathematical operation that yields a scalar quantity. It is calculated by multiplying the magnitudes of two vectors and the cosine of the angle between them. The formula for the scalar product of two vectors A and B is A · B = |A| |B| cos(θ), where θ is the angle between the vectors.
2. What is the vector product of two vectors?
The vector product, also known as the cross product, is a mathematical operation that yields a vector quantity. It is calculated by taking the cross product of the magnitudes of two vectors and the sine of the angle between them. The formula for the vector product of two vectors A and B is A × B = |A| |B| sin(θ) n, where θ is the angle between the vectors and n is a unit vector perpendicular to both A and B.
3. How is the scalar product related to the angle between two vectors?
The scalar product of two vectors is directly related to the angle between them. The scalar product is equal to the product of the magnitudes of the vectors and the cosine of the angle between them. If the scalar product is positive, the angle between the vectors is acute. If the scalar product is negative, the angle between the vectors is obtuse. And if the scalar product is zero, the vectors are perpendicular to each other.
4. What does the vector product of two vectors represent?
The vector product of two vectors represents a new vector that is perpendicular to both of the original vectors. This new vector's magnitude is equal to the product of the magnitudes of the original vectors and the sine of the angle between them. The direction of the vector product can be determined using the right-hand rule, where the thumb points in the direction of the vector product when the fingers curl from the first vector to the second vector.
5. In what situations are the scalar and vector products used?
The scalar product is commonly used in physics and engineering to calculate work done, find projections of one vector onto another, determine angles between vectors, and solve problems involving forces and displacements. On the other hand, the vector product is frequently used to calculate torque, determine the area of a parallelogram formed by two vectors, find the direction of magnetic fields, and solve problems involving angular momentum and rotational motion.
205 videos|264 docs|139 tests
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