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How do you calculate the projection of a vector onto another vector?
Wiki User
∙ 14y ago
If A and B are two vectors, the projection (C) of A on B is the vector that has the same slope as B with the length:
To calculate C use the following property of the dot product:
Using the above equation:
Multiply and divide by | B | at the same time:
In the resulting fraction, the top term is the same as the dot product, hence:
To find the length of | C | with an unknown θ, and unknown direction, multiply it with the unit vector B:
giving the final formula:
taken from: http://en.wikipedia.org/wiki/Vector_projection
Wiki User
∙ 14y ago
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Why you only use cosine for scalar product?
That is how the scalar product is defined. Also, the projection of one vector onto another at an angle to it is directly proportional to the cosine of that angle.
Why is shape of satellite footprint is irregular?
It is not irregular: it is simply the projection of a regular curve onto the surface of a sphere.
What does the top down view of a solid figure mean?
It is the two-dimensional image of the solid figure when it is viewed from points above the object. In mathematical terms (projective geometry), it is the projection of the figure onto a horizontal plane using the point at infinity as the centre of projection.
Can a vector have 0 component along a line and still have non zero magnitude?
Huh?I have been kicking around your question in my mind for five minutes trying to figure out an answer or a way to edit your question into an unambiguous form, but I'm stumped. I don't know what you mean by "zero component along a line."If you look at the representation of a vector on paper using a Cartesian coordinate system -- in other words, one using x and y axes -- the orthogonal components of the vector are the projections of the vector on the x and y axes. If the vector is parallel to one of the axes, its projection on the other axis will be zero. But the vector will still have a non-zero magnitude. Its entire magnitude will project on only one axis.But a vector must have magnitude AND direction. And if it has zero magnitude, its direction cannot be determined.Still trying to make heads or tails out of your question.......If you draw a random vector on a Cartesian grid, it will have an x component and a y component, which are both projections of the original vector upon the axes. However, it could also be represented by projecting it onto a new set of orthogonal axes -- call them x' and y' -- where the x' axis is oriented to be parallel to the original vector and the y' vector is perpendicular to it. In that case, the x' component will have a magnitude equal to the magnitude of the original vector -- in other words, a non-zero value along a line parallel to the x' axis -- and a zero magnitude in the y' direction.
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Don't stop believing'… hold onto that feelin'
Why you only use cosine for scalar product?
That is how the scalar product is defined. Also, the projection of one vector onto another at an angle to it is directly proportional to the cosine of that angle.
The projection of a point onto a line is a?
Point.
What are the shadows cast by other shapes onto surfaces called?
A shadow can be called a projection, if you are discussing the way one shape can be transformed into another as a shadow.
What type of projection is made by projecting a globe onto a cylinder?
mercator .
Maps can be made by projecting Earth's spherical grid onto a?
That would depend on the type of map. A Mercator projection projects the Earth onto a cylinder, causing distortions at the poles. A "conic" projection projects the Earth onto a cone. And there are special purpose maps that project the Earth onto a plane.
What cellular organelle is a projection that moves substances onto epithelial surfaces?
Cilia
Is a projection a way of mapping the flat surface of Earth onto a round globe?
Yes they do
What is the size of Congo in mercator projection?
A mercator projection is defined as a projection of a map of the world onto a cylinder in such a way that all the parallels of latitude have the same length as the equator, used especially for marine charts and certain climatological maps. Congo, as depicted in mercator projection, is small.
What is planar projection map good for?
A planar projection map is a map projected onto a plane (flat surface). The details of the globe are a rectangular shaped map that is on a flat surface.
Why is shape of satellite footprint is irregular?
It is not irregular: it is simply the projection of a regular curve onto the surface of a sphere.
52 RCA HDTV model HD52W59 is it front or rear projection?
This Television is a rear projection CRT display. Front projection uses a self contained "Projector" usually hanging from the ceiling and shoots the image onto a fabric screen or wall. The projector in the RCA HD52W59 is actually inside the base of the unit and the projected image is bounced off of a mirror and onto the back of the screen There are many types or Rear Projection displays: CRT, LCD, DLP, LED and Laser.
What is projection of line?
The line joining the feet of the perpendiculars drawn from all the points of the line onto a preselected plane.
