Answer to Question #154084 in Calculus for zeeshan wahab

Question

Describe the uses of Vector Calculus in real life and in Engineering field (any five)

Answer 1

Vectors sound complicated, but they are common when giving directions. For example, telling someone to walk to the end of a street before turning left and walking five more blocks is an example of using vectors to give directions.

Navigating by air and by boat is generally done using vectors. Planes are given a vector to travel, and they use their speed to determine how far they need to go before turning or landing. Flight plans are made using a series of vectors.

Sports instructions are based on using vectors. Wide receivers playing American football, for example, might run a route where they run seven yards down the field before turning left 45 degrees and running in that direction. Sports commentary also depends on vectors. Only a few sports have fields with grids, so discussions revolve around the direction and speed of the player.

Vector calculus is used extensively in many branches of physics. Basic to professional level familiarity with the subject is necessary for (among others)

1. Classical Mechanics, most notably Fluid Mechanics.
2. Electrodynamics — you can't do anything without vector calculus.
3. Subjects like General Relativity and Quantum Mechanics also use things related to simple vector calculus — Tensor calculus and vector spaces.
4. Modern-day computer programming and graphics