Yeshua asked in Science & MathematicsMathematics · 8 months ago

# Help on vectors?

May someone explain me on a simple way what vector projection, vector comp, dot product, and cross product are? May you add some examples? What do vectors describe? know how to compute them, but I want to know the idea behind them. (If you add some real applications, it wil be better)

Relevance
• 8 months ago

The definition of "vector" is, a quantity having direction as well as magnitude, especially as determining the position of one point in space relative to another. In the real world, in terms of engineering, "vectors" are the flight paths of airplanes in the sky. A flight navigator and ground control in the control tower need to figure out the vectors of the plane at 35000 feet in terms of height from the ground, distance from the airport, but the plane's actual location in the sky and the flight path it is taking in comparison to other planes in the same airspace. Where I live, overhead are several airplanes crossing paths, luckily at different altitudes. One plane is coming from the east and going west on a landing descent to the airport 100 miles away from my house, it is coming in at a trajectory descent of going down one foot every 200 feet over a distance of 100 miles. Because its flight path crosses over a populated valley where towns are spread out over a distance and 5 different local municipal airports of small twin engine and single engine aircraft flying up to 10,000 feet, the big airplane coming in for a landing needs to descend and not hit another plane in its path on its descent, The "Vectors" are the plane descending on its trajectory towards the airport, the plane's position in distance from the ground directly perpendicular below, the position in the air in relation to any other aircraft in the same airspace, and distance from the airport. An Air traffic controller has to identify all the aircraft in the same airspace, know each airplane's speed, trajectory and altitude, and know which plane can move out of the way so when the planes pass each other one is flying at 35000 feet while another plane crosses its path underneath at 25000 feet, but at the speeds of the planes, one plane might have to ascend to 38000 over a 100-mile distance coming from the south to the north while the plane coming in for a landing going east to west descends over a 100-mile distance. The vectors needing to be calculated are the planes speeds, rate, time, the distance from the ground, the distance from each other, and the distance of each plane from any other low-flying local aircraft. (This is why we don't have flying cars yet! The calculations to avoid in-air crashes are intense!) The next situation for vectors are in the design of the airplane cabin. The design engineer needs to know the strength of the materials used to build the airplane cabin at sea level, but also the strength of the materials under the atmospheric pressure at 35000 feet. There is the tensile strength of the structure of the airplane cabin lengthwise from tip to end, plus the interior pressure at each point inside the cabin at 35000 feet to match the exterior atmospheric pressure outside, and how much pressure force needs to be generated inside the airplane cabin that is equal to the outside pressure at any altitude at any time during the flight. Hence the intense math in an Engineering program! Good luck to you in continuing your studies!

• Luca
Lv 6
8 months ago

At what level? Early high school/end high school/undergrad?

• Mark
Lv 7
8 months ago

Vectors record your speed and where you're going; speed just indicate how fast you are going.