The gradient of a scalar field is a vector. Hence explain how to produce a vector from a scalar field.
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scalar is an entity which only has a magnitude – no direction. Examples of scalar quantities include mass, electric charge, temperature, distance, etc.
A vector, on the other hand, is an entity that is characterized by a magnitude and a direction. Examples of vector quantities are displacement, velocity, magnetic field, etc.
A scalar can be depicted just by a number, for e.g. a temperature of 300 K. On the other hand, vectorial quantities like acceleration are usually denoted by a vector. Given a vector VV, the magnitude of the corresponding quantity can be calculated as the magnitude of the vector itself ∥V∥‖V‖, while the direction would be specified by a unit vector in the direction of the original vector, V^=V∥V∥V^=V‖V‖.
For example, consider a displacement of (3i^+4j^+5k^)(3i^+4j^+5k^) m, where , as per standard convention, i^i^, j^j^ and k^k^ represent unit vectors in the XX, YY and ZZ directions respectively. Therefore, it can be concluded that the distance traveled is ∥3i^+4j^+5k^∥‖3i^+4j^+5k^‖ m = 52–√52 m. The direction of travel is given by the unit vector 352√i^+452√j^+552√k^352i^+452j^+552k^.
A vector, on the other hand, is an entity that is characterized by a magnitude and a direction. Examples of vector quantities are displacement, velocity, magnetic field, etc.
A scalar can be depicted just by a number, for e.g. a temperature of 300 K. On the other hand, vectorial quantities like acceleration are usually denoted by a vector. Given a vector VV, the magnitude of the corresponding quantity can be calculated as the magnitude of the vector itself ∥V∥‖V‖, while the direction would be specified by a unit vector in the direction of the original vector, V^=V∥V∥V^=V‖V‖.
For example, consider a displacement of (3i^+4j^+5k^)(3i^+4j^+5k^) m, where , as per standard convention, i^i^, j^j^ and k^k^ represent unit vectors in the XX, YY and ZZ directions respectively. Therefore, it can be concluded that the distance traveled is ∥3i^+4j^+5k^∥‖3i^+4j^+5k^‖ m = 52–√52 m. The direction of travel is given by the unit vector 352√i^+452√j^+552√k^352i^+452j^+552k^.
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