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