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Examples: Vector Operations Video Lecture | Mathematics (Maths) Class 12 - JEE

205 videos|264 docs|139 tests

FAQs on Examples: Vector Operations Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What are the basic operations that can be performed on vectors?
Ans. The basic operations that can be performed on vectors include addition, subtraction, scalar multiplication, dot product, and cross product.
2. How can addition of vectors be performed?
Ans. Addition of vectors is performed by adding the corresponding components of the vectors. For example, if we have two vectors A = (a1, a2, a3) and B = (b1, b2, b3), then their sum is given by A + B = (a1 + b1, a2 + b2, a3 + b3).
3. What is the dot product of two vectors and how is it calculated?
Ans. The dot product of two vectors A and B is a scalar quantity that is calculated by multiplying the corresponding components of the vectors and then summing up the results. It is denoted by A · B or A · B = a1b1 + a2b2 + a3b3.
4. How can the cross product of two vectors be calculated?
Ans. The cross product of two vectors A and B is a vector quantity that is calculated by using the determinant of a 3x3 matrix. The cross product is given by A × B = (a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1).
5. What is scalar multiplication of a vector and how is it performed?
Ans. Scalar multiplication of a vector involves multiplying the vector by a scalar quantity. Each component of the vector is multiplied by the scalar value. For example, if we have a vector A = (a1, a2, a3) and a scalar k, then the scalar multiplication is given by kA = (ka1, ka2, ka3).
205 videos|264 docs|139 tests
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