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?