Vector Projection

Key Questions

• How does a vector differ from its projection?

  A vector is specified by its components along the coordinate axes in a particular coordinate system.
  A vector projection of a vector A along some direction is the component of the vector along that direction.
  If A makes an angle `theta` with the direction in which we are to find it's projection and it's magnitude `A`, the projection is given as `A cos theta`.

  Aritra G. · 2 · Jul 26 2015
• What are vector projections used for?

  Vector projections are used for determining the component of a vector along a direction.

  Let us take an example of work done by a force F in displacing a body through a displacement d.
  It definitely makes a difference, if F is along d or perpendicular to d (in the latter case, the work done by F is zero).

  So, let us for now assume that the force makes an angle `theta` with the displacement. In this case the component of force along displacement does all the work.
  The component of F along d is `F Cos theta` , which is nothing other than the projection of F along d.

  Thus, for a general case, work done is given as,

  `W = F Cos theta * d`

  Which can be written concisely as,

  `W` = F . d

  Aritra G. · 1 · May 31 2015
• What is vector projection?

  Answer:

  A vector projection along any direction is the component of a given vector along that direction.

  Explanation:

  If we have to determine the vector projection of vector A with modulus `A` along a direction with which the vector A makes an angle `theta`, the projection is given as, `A Cos theta`

  Aritra G. · 2 · Jul 26 2015
• How do I determine the vector projection of a vector?

  Answer:

  Please see the explanation below

  Explanation:

  The vector projection of `vecb` onto `veca` is

  `proj_(veca)vecb=(veca.vecb)/(|veca|^2)veca`

  Calculate the dot product

  `=veca.vecb`

  and calculate the modulus of `veca`

  `=||veca||`

  Narad T. · 1 · Aug 4 2018

• What is the vector projection formula?
• What are vector projections used for?
• How does a vector differ from its projection?
• How do I find the orthogonal vector projection of `vec{a}` onto `vec{b}`?
• How do I determine the vector projection of a vector?
• What is vector projection?
• How do I find the orthogonal projection of a vector?
• How do I find the orthogonal projection of two vectors?
• How do you find the vector `C` that is perpendicular to `A-> -3x+9y-z=0` and which vector `C` has a magnitude of `1`?
• Question #8f5e6
• In a `DeltaABC`, `b=10m`, `c=21m` and `/_A=58^o`. What is the area of the triangle?
• How do you find the projection of u onto v given `u=<2,2>` and `<v=6,1>`?
• How do you find the projection of u onto v given `u=<3, 15>` and `<v=-1, 5>`?
• How do you find the projection of u onto v given `u=<4, 2>` and `v=<1, -2>`?
• How do you find the projection of u onto v given `u=<0, 3>` and `v=<2, 15>`?
• How do you find the projection of u onto v given `u=<-3, -2>` and `v=<-4, -1>`?
• How do you determine whether u and v are orthogonal, parallel or neither given `u=<-12, 30>` and `v=<1/2, -5/4>`?
• How do you determine whether u and v are orthogonal, parallel or neither given `u=<3, 15>` and `v=<-1, 5>`?
• How do you determine whether u and v are orthogonal, parallel or neither given `u=1/4(3i-j)` and `v=5i+6j`?
• How do you determine whether u and v are orthogonal, parallel or neither given `u=i` and `v=-2i+2j`?
• How do you determine whether u and v are orthogonal, parallel or neither given `u=2i-2j` and `v=-i-j`?
• How do you determine whether u and v are orthogonal, parallel or neither given `u=<costheta, sintheta>` and `v=<sintheta, -costheta>`?
• How do you find the projection of u=<4,8> onto v=<-1,2>?
• How do you find the projection of u=<62,21> onto v=<-12,4>?
• Question #8e005
• What are eigenvectors and eigennumbers?
• How can I find the projection of a vector onto a subspace?
• Find a vector of magnitude 4 unit and parallel to vector I + j?