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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.
Why you are using cosine function in dot product of two vectors?
It comes from the Law of Cosines. * * * * * For any two vectors A and B, the projection of A onto B, that is, the component of A along B, is ab.cos(x) where x is the angle between the two vectors. By symmetry, this is also the projectoin of B onto A.
Can a vector have a component greater than the magnitude of the vector?
No, a vector component is a projection of the vector onto a specific direction. It cannot have a magnitude greater than the magnitude of the vector itself.
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.
Can a single vector be replaced by two vectors in the x and y directions.?
Yes, a single vector can be represented by two vectors in the x and y directions using vector decomposition. This is known as resolving a vector into its components and can be done using trigonometry. The x-component corresponds to the projection of the vector onto the x-axis, and the y-component corresponds to the projection of the vector onto the y-axis.
What is a vector times iteself?
When a vector is multiplied by itself, it is known as the dot product. The result is a scalar quantity, which represents the projection of one vector onto the other. This operation is different from vector multiplication, where the result is a new vector.
What is component in vector?
In vector terms, a component refers to the portion of the vector along a particular direction or axis. It is the projection of the vector onto that specific direction. For example, a vector in two dimensions can be broken down into its horizontal and vertical components.
What is the difference between scalar and vector products of two vectors?
The scalar product (dot product) of two vectors results in a scalar quantity, representing the magnitude of the projection of one vector onto the other. The vector product (cross product) of two vectors results in a vector quantity that is perpendicular to the plane formed by the two input vectors, with a magnitude equal to the area of the parallelogram they span.
The projection of a point onto a line is a?
Point.
How a vector can be express in term of its rectangular component?
A vector can be expressed in terms of its rectangular components by breaking it down into its horizontal and vertical components. These components represent the projection of the vector onto the x and y axes. The vector can then be expressed as the sum of these components using the appropriate unit vectors (i and j for x and y directions, respectively).
What is it called when someone projects their own personality or feelings onto or through someone or something else?
That is known as projection. It is a defense mechanism where an individual attributes their own emotions or traits onto another person or object.
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?
The type of projection is called a cylindrical projection. This process involves wrapping the globe's surface around a cylinder to create a flat map.
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.
