231.13.3.33 calculate the proj_u, and scal_u

  • MHB
  • Thread starter karush
  • Start date
In summary, the purpose of calculating proj_u and scal_u is to determine the projection of a vector onto another vector and the scalar component of that projection. This is done using vector operations, where the projection of vector a onto vector b is given by proj_u = (a · b / |b|²) * b and the scalar component is calculated as scal_u = a · b / |b|. This calculation can be applied to vectors in any dimension and has various real-world applications, such as in physics, engineering, computer graphics, and data analysis. The main difference between proj_u and scal_u is that the former is a vector while the latter is a scalar value.
  • #1
karush
Gold Member
MHB
3,269
5
$\tiny{231.13.3.33}$
$\textsf{For the vectors
$u=\langle -3,0,1 \rangle$,
$v=\langle 1,2,-2 \rangle$,
calculate the $proj_u$, and $scal_u$} $

$\textit{being on my own can't find an example for this ?}$😰
 
Physics news on Phys.org
  • #2
If you are talking about vector and scalar projections of a vector on another vector, then you may refer to Wikipedia.
 
  • #3
I would prefer a textbook...
 

FAQ: 231.13.3.33 calculate the proj_u, and scal_u

What is the purpose of calculating proj_u and scal_u?

The purpose of calculating proj_u and scal_u is to determine the projection of a vector onto another vector and the scalar component of that projection. This calculation can be useful in various mathematical and scientific applications, such as in physics and engineering.

How is the proj_u and scal_u calculated?

The proj_u and scal_u are calculated using vector operations. The projection of vector a onto vector b is given by proj_u = (a · b / |b|²) * b, where · represents the dot product and |b| represents the magnitude of vector b. The scalar component is then calculated as scal_u = a · b / |b|.

Can proj_u and scal_u be calculated for vectors in any dimension?

Yes, proj_u and scal_u can be calculated for vectors in any dimension. The formula remains the same regardless of the number of dimensions.

What is the difference between proj_u and scal_u?

The projection of a vector onto another vector gives the component of the original vector in the direction of the second vector. On the other hand, the scalar component is the magnitude of this projection. In other words, the proj_u is a vector while the scal_u is a scalar value.

What are some real-world applications of proj_u and scal_u?

Some real-world applications of proj_u and scal_u include calculating forces in physics problems, finding the components of a force acting on an object, and analyzing motion in engineering problems. These calculations can also be used in computer graphics and data analysis.

Similar threads

MHB S6.793.12.4.33 Find the volume of the parallelepiped
Replies
3
Views
1K
MHB S4.13.t.71 angles of triangle PQR
Replies
5
Views
4K
MHB 243.12.5.26 Show That The Line And The Plane Are Not Parallel.
Replies
1
Views
1K
MHB 231.12.3.63 Determine the smallest distance between point and line
Replies
1
Views
1K
MHB 231.12.3.65 Determine the smallest distance between a point and a line
Replies
8
Views
2K
MHB S6.12.25 find v in component form
Replies
2
Views
1K
MHB Are the Given Planes Parallel, Perpendicular, or Intersecting at an Angle?
Replies
4
Views
2K
MHB 12.3.63 Determine the smallest distance between point and a line
Replies
6
Views
2K
MHB S4.854.13.5.47 Find symmetric equations, angle between the planes
Replies
4
Views
2K
MHB S6.12.3.17 Find the angle between the vectors
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top