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Vector Algebra & Cartesian Coordinate System- 2 Video Lecture | Crash Course for IIT JAM Physics
FAQs on Vector Algebra & Cartesian Coordinate System- 2 Video Lecture - Crash Course for IIT JAM Physics
| 1. What is vector algebra and how is it related to the Cartesian coordinate system? |  |
Ans. Vector algebra is a branch of mathematics that deals with mathematical operations on vectors, which are quantities that have both magnitude and direction. The Cartesian coordinate system is a mathematical tool used to represent points in space using a set of perpendicular axes. Vector algebra is closely related to the Cartesian coordinate system as it allows for the representation and manipulation of vectors within this coordinate system.
| 2. How do you perform vector addition and subtraction in vector algebra? | |
Ans. In vector algebra, vector addition and subtraction are performed by adding or subtracting the corresponding components of the vectors. For example, to add two vectors A = (A₁, A₂, A₃) and B = (B₁, B₂, B₃), we add their respective components and obtain the resultant vector R = (A₁ + B₁, A₂ + B₂, A₃ + B₃). Similarly, vector subtraction is carried out by subtracting the corresponding components of the vectors.
| 3. What is the dot product in vector algebra and how is it calculated? | |
Ans. The dot product, also known as the scalar product, is an operation in vector algebra that combines two vectors to obtain a scalar quantity. It is calculated by taking the product of the magnitudes of the vectors and the cosine of the angle between them. Mathematically, the dot product of two vectors A and B is given by the equation A · B = |A| |B| cosθ, where |A| and |B| are the magnitudes of the vectors and θ is the angle between them.
| 4. How can vector algebra be used to solve geometric problems in the Cartesian coordinate system? | |
Ans. Vector algebra can be used to solve geometric problems in the Cartesian coordinate system by representing geometric figures and transformations as vectors. For example, the position vector of a point P in the Cartesian coordinate system can be used to determine its coordinates. Additionally, vector operations such as dot product, cross product, and magnitude calculations can be used to find angles, distances, and areas in geometric problems.
| 5. What is the cross product in vector algebra and how is it calculated? | |
Ans. The cross product, also known as the vector product, is another operation in vector algebra that combines two vectors to obtain a new vector that is perpendicular to both input vectors. It is calculated using the determinant of a 3x3 matrix formed by the components of the vectors. Mathematically, the cross product of two vectors A and B is given by the equation A × B = (A₂B₃ - A₃B₂, A₃B₁ - A₁B₃, A₁B₂ - A₂B₁). The resulting vector is orthogonal to both A and B.
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