VECTORS

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Unit-2VECTORS

Presentation

Start!

2- History

1- introduction

3- Sports

index

6- Conclusion

5- Aviation

4- Gaming

MATHEMATICS GIVES US HOPE THAT EVERY PROBLEM HAS A SOLUTION

01

history of vectors

History

The word vector has been derived from a Latin word Vectus, which means “to carry”. Around 1800 when Caspar Wessel and Jean Robert Argand

William Rowen Hamilton an Irish mathematician was the first to use the term vector for a directed line segment in his book Lectures on Quaternions (1853). Hamilton’s method of quaternions (an ordered set of four real numbers given as:

following certain algebraic rules) was a solution to the problem of multiplying vectors in three dimensional space.

history

In the 1880, Josaih Willard Gibbs (1839-1903), an American physicist and mathematician, and Oliver Heaviside (1850-1925), an English engineer, created what we now know as vector analysis, essentially by separating the real (scalar) part of quaternion from its imaginary (vector) part. In 1881 and 1884, Gibbs printed a treatise entitled Element of Vector Analysis. This book gave a systematic and concise account of vectors

Real Life Applications

• Force, velocity and torque
• Military usage
• Projectile
• Sports
• Gaming
• Cricket
• Aviation etc.

Vectors in Sports

BILLIARDS In billiard game, rolling ball is moving toward a glancing collision with a stationary billiard ball. On impact, the moving ball transfers some of its momentum to the stationary ball, and both roll away from the collision in different directions. Following the impact, both balls have velocity and hence momentum. With an understanding of vectors, billiards players can predict where both balls will go following a collision, allowing them to sink more target balls while keeping the cue ball safely on the table.

Vectors in sports

CRICKET In a cricket game, player moving a certain direction for a specific distance to reach a high fly ball before it touches the ground. The fielder can't just run directly for where he sees the ball first or he is going to miss it. The player must anticipate what direction and how far the ball will be from him when it drops and move to that location to have the best chance of catching the ball.

Vectors in Gaming

In Games, vectors are used to store positions, directions and velocities. The position vectors indicates how far the object is, the velocity vector indicates how much time it will take or how much force we should give and the direction vector indicates in which way we should apply the force.

Vectors in Aviation

Aircraft Navigation- the subject of getting from a dept point to a destination in the least possible time without losing your way. Aircraft’s speed is greatly enhanced/diminished by the wind. Consideration of ground speed and air speed. Ground speed, the speed at which an aircraft is moving w.r.t. the ground. Air speed, the speed of an aircraft in relation to the surrounding air. Wind speed, the physical speed of the air relative to the ground. Air, ground and wind speeds are all vectors .

Vectors in Aviation

+ info

Conclusion

To conlcude, Numerous use in fields of Physics, Mathematics and Engineering. Interplay of two or more quantities in Physics. Used for the Scalar triple product. Vectors form an inevitable part of our lives.

Thanks!

• Aalia Fatema Dandawala - C080
• Christopher Dsouza - C079
• Yazad Bardoliwala - C078