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For example, imagine a submarine is at a dangerous depth and we are interested in that fact. You might ask:

What is the temperature down there? In case they freeze down there.

What is the pressure on the hull? In case it is crushed.

What is the speed of the submarine? So they can get out of trouble quickly.

Now, the answers to the first two questions will satisfy your curiosity. They probably will freeze at -12 degrees but the hull can withstand a pressure of 12,000 megapascals, but told that the sub was going at 2 knots wouldn't help. You'd probably ask again, "Up, down, backwards or forwards?"

Pressure and temperature are NOT VECTORS in physics. They just need a quantity to show all about them. VECTORS on the other hand, like velocity, have quantity and also direction, and both of these are necessary to show them. Two knots down is very different from two knots up.

You might argue that the pressure on the top of the sub is down and the pressure on the bottom of the sub is up. This is true, but we know that information without anybody looking or telling us. It's not necessry to be told that. The direction a pressure acts is defined by the situation, but a velocity isn't given by the shape of the object or the direction it's facing.

Therefore, Vectors are qualities with quantity and direction.

For example, suppose you are in a car going at 60 mph due North and there is a cross-wind blowing at 20 mph from the west. What will be the speed and direction of the airflow over the car? If you do that, you're doing a Vector algebra sum.

Q: What is a vector in mathematics?

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A vector of magnitude 1.

There does not seem to be an under vector room, but there is vector space. Vector space is a structure that is formed by a collection of vectors. This is a term in mathematics.

Linear Algebra

in mathematics the cross products are the binary operation on two vectors in a 3dimensional Euclidean space that results in another vector which is perpendicular to the containing the 2 inputs vector.

i is often used to denote the [imaginary] square root of -1. It can also be the unit vector in the horizontal direction.

Related questions

A vector of magnitude 1.

There does not seem to be an under vector room, but there is vector space. Vector space is a structure that is formed by a collection of vectors. This is a term in mathematics.

Linear Algebra

A zero vector is a vector whose elements are all zero. It has no direction or magnitude, and does not change the position of any point it is added to. In mathematics, it is often denoted as 0.

A unit vector is a vector with a magnitude of 1. It is often used to indicate direction without influencing the scale of a vector. Unit vectors are important in mathematics, physics, and engineering for simplifying calculations involving vectors.

A vector has magnitude and direction, but no inherent color as it is a mathematical concept representing a quantity with both. The idea of a vector being a certain color is not applicable in the context of mathematics.

if a column vector such as x y is multiplied by a raw vector such as ( 2 0), ( 2 o) x y = 2x so 2x is the image of x y

The line above a letter in mathematics means a vector whose mane is the letter. So it is pronounced "vector a"

Vector.

They are used in a types of mathematics and can represent anything with a direction and a magnituted. Examples are temperature changes, directions you move, but many examples are far more abstract. In fact every ordered pair of numbers, (a,b) can be thought of as a vector with the origin (0,0) being one point and (a,b) being the other end of the vector. We should can the point tip and tail of the vector. However, remember, the line segment with an arrow is just a representation of the vector, it is not the vector itself.

No, possession of magnitude and direction alone is not always sufficient for calling a quantity a vector. A vector must also obey the rules of vector addition and scalar multiplication to be considered a true vector in physics and mathematics.

U. Koschorke has written: 'Differential Topology' -- subject(s): Congresses, Differential topology 'Vector fields and other vector bundle morphisms' -- subject(s): Singularities (Mathematics), Vector bundles, Vector fields