What is Components of vectors: Definition and 17 Discussions

In mathematics, physics and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a ray (a directed line segment), or graphically as an arrow connecting an initial point A with a terminal point B, and denoted by


{\displaystyle {\overrightarrow {AB}}}
.A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier". It was first used by 18th century astronomers investigating planetary revolution around the Sun. The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from A to B. Many algebraic operations on real numbers such as addition, subtraction, multiplication, and negation have close analogues for vectors, operations which obey the familiar algebraic laws of commutativity, associativity, and distributivity. These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space.
Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can still be represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.

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  1. L

    Confused about resolving Tension and Weight

    Calculations with 1: T1sintheta + T2sintheta = W T1costheta = T2costheta Calculations with 2: Wsintheta = T1 Wcostheta = T2 These are not equivalent. Can someone point out the flaw in my logic? Edit: System is in equilibrium!
  2. Hawkingo

    B Can a Scalar Operate with a Vector Algebraically?

    Let ##\vec { A }## = ##a \dot { i } + b \hat { j } + c \hat { k }## My question is "is ##\frac { 1 } { \vec { A } }## is a vector or not and if yes then what is it's components?"
  3. T

    How Do You Calculate the Velocity of a Stone in Projectile Motion?

    Homework Statement Astone is thrown horizontally with an initial velocity of 5 metres per second. What is the magntude and direction of its velocity 0.2s later? Take the acceleration of free fall to be 9.8 metres per second squared and ignore friction. Homework EquationsThe Attempt at a...
  4. G

    Solve for Angle in 2D Projectile Motion Problem | Neglecting Air Resistance

    Homework Statement There are two cliffs separated by 40 meters (horizontal displacement). An arrow is shot from a bow at an angle and a velocity of 90 m/s. The arrow takes 0.75 seconds to arrive at the other cliff. What is the angle at which the arrow was released? Neglect air resistance...
  5. J

    Finding Your Way Home: Vector Components and Trigonometry

    Homework Statement Finn is lost in the woods, trying to find his way back home which he knows is 7.00 km at a 120.0° angle from his current location. He decides to travel 2.00 km at a 40.0° angle followed by another 5.00 km at a 100° angle. 1) What is his current location using a km coordinate...
  6. P

    Components of vectors (polar coordinates)

    I have always been under the impression that a vector is not "fixed" in space. Given any vector, we could just move it around and it would still have the same components (in a cartesian coordinate system). What confuses me, however, is how we define the components of a vector in polar...
  7. W

    Finding Resultant Vector C with Given Vectors A and B

    Homework Statement Let resultant vector A = 17 i hat - 42 j hat and resultant vector B = 31 j hat + 18 k hat. Find the resultant vector C such that the sum of resultant vector A, B and C equals resultant vector zero. Find the i,j and k components of resultant vector C. Homework Equations...
  8. K

    Calculating the components of vectors

    Vector A is in the direction 41.0 degrees clockwise from the y-axis. The x component of A is = -15.0 . A)What is the y component of vector A? B)What is the magnitude of vector A? I got -13.0m for part a, and 19.8m for part b, but mastering physics says they are wrong. Any ideas?
  9. S

    Numerical problem on vector algebra - components of vectors

    Homework Statement Two beetles run across flat sand, starting at the same point. Beetle 1 runs 0.50m due east, then 0.80m at 30° north of due east. Beetle 2 also makes two runs; the first is 1.6m at 40° east of due north. What must be (a) the magnitude and (b) the direction of its second run...
  10. E

    Finding Components of Vectors in a Crystal Lattice

    Homework Statement Be the vectors a, b, c such as: | a | = | b | = | c | = 10.5 Angstron The angles between these vectors are: alpha = beta = gamma = 109.5 degree These vectors represent the lattice vectors of a crystal. Find out their components (a_1, a_2, a_3, b_1...
  11. B

    Find components of vectors on F

    1. Problem is pictured here. http://engineeringhomework.net/statics/hw1p14.html" I have already found the x and y components, but I don't know how to get the u and v as shown.
  12. G

    Need help with components of vectors

    Homework Statement 1. Given the following force vectors: A is 27 lb at an angle of 27° clockwise from the +x-axis, and B is 44 lb at an angle of 45° clockwise from the +y-axis. (a) Make a sketch and visually estimate the magnitude and angle of the vector C such that 2A+ C − B results in a...
  13. X

    What Are the Components of These Two Vectors?

    Homework Statement Vector A is 3.28 m long and points along the x axis. Vector B is 190.6 cm long and points at +25° to the positive x axis (a) What are the components of Vector A? (b) What are the components of Vector B? (c) What is the resultant of these two vectors in terms of...
  14. N

    Finding the Shortest Path in a Vector Space

    Homework Statement A room has dimensions 2.95 m (height) × 4.68 m × 6.19 m. A fly starting at one corner flies around, ending up at the diagonally opposite corner. (a) What is the magnitude of its displacement? (b) If the fly walks rather than flies, what is the length of the shortest path...
  15. P

    Calculating Acceleration of a Barge Being Pulled by a Horse Along a Canal

    Can anyone help me with this question? I would appreciate it. A horse pulls a barge of mass 5000 kg along a canal using a rope 10 m long. The rope is attached to a point on the barge 2m from the bank. As the barge starts to move, the tension in the rope is 500 N. Calculate the barge's initial...
  16. S

    Why you can't mix x and y components of vectors?

    Hi. Does anyone know of a proof that explains why you can't mix x and y components of vectors? For example you know how if you are solving a physics problem you have to break things up into x any y components (eg: velocity). My physics teacher wanted us to find a proof online that explained why...
  17. R

    Vector Components and Flight Paths

    A commuter airplane starts from an airport located at the origin. first it flies to city "A" located a =110km away from the airport in a direction alpha = 36 degrees North of East. Next it flies b =61.8km beta=38 degrees west of north to city "B". Finally it flies c=168 km due West to city "C"...