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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
What else can I help you with?
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 is the difference between first and third angle protection?
First angle projection and third angle projection are two methods of orthographic projection used in technical drawings. In first angle projection, the object is placed in the first quadrant, meaning the view is projected onto the plane behind the object, resulting in the top view appearing below the front view. In contrast, third angle projection places the object in the third quadrant, with the views projected onto the planes in front of the object, making the top view appear above the front view. These conventions are used to standardize how drawings are interpreted, with first angle commonly used in Europe and third angle in the United States.
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.
What are the types of oblique projection?
Oblique projection is primarily categorized into two types: cavalier and cabinet projections. Cavalier projection maintains the full scale of depth, resulting in a more distorted appearance, while cabinet projection reduces the depth scale by half, providing a more realistic view. Both types project the object onto a plane at an angle, typically 45 degrees, allowing for a clear representation of the object's dimensions and features.
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.
What are the structure of projection?
The structure of projection typically involves three main components: the subject, the predicate, and the object. In a psychological context, projection refers to attributing one’s own thoughts or feelings onto others, often as a defense mechanism. In a mathematical or geometric context, projection can refer to mapping points from one space onto another, preserving certain properties. Each type of projection serves to convey information or influence perception in different ways.
How a vector can be express in term of its rectangular component?
A vector can be represented in terms of its rectangular components for example : V= Ix + Jy + Kz I, J and K are the rectangular vector direction components and x, y and z are the scalar measures along the components.
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 is it called when someone projects their own personality or feelings onto or through someone or something else?
when someone uses their own personality onto or through someone else, that is called projection of emotions or ideas or characteristics through someone else.
How to find the dot product of two vectors?
To find the dot product of two vectors, you multiply the corresponding components of the vectors and then add the results together. This gives you a single scalar value that represents the magnitude of the projection of one vector onto the other.
