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Given one vector a, any vector that satisfies a.b=0 is orthogonal to it. That is a set of vectors defining a plane orthogonal to the original vector.
The set of vectors defines a plane to which the original vector a is the 'normal'.
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What is a vector which is orthogonal to the other vectors and is coplanar with the other vectors called?
In a plane, each vector has only one orthogonal vector (well, two, if you count the negative of one of them). Are you sure you don't mean the normal vector which is orthogonal but outside the plane (in fact, orthogonal to the plane itself)?
A vedtor which is perpendicular to every vector?
The zero vector is not perpendicular to all vectors, but it is orthogonal to all vectors.
How do you name the direction of a vector?
The direction of a vector is defined in terms of its components along a set of orthogonal vectors (the coordinate axes).
What is the maximun no of components into which a vector can be split?
There is no maximum. A vector can be defined for a hyperspace with any number of dimensions. Such a hyperspace can be described using an orthogonal system of axes and the vector can be split into its components along each one of these axes.
Can a vector have zero magnitude if one of its components is nonzero?
A vector comprises its components, which are orthogonal. If just one of them has magnitude and direction, then the resultant vector has magnitude and direction. Example:- If A is a vector and Ax is zero and Ay is non-zero then, A=Ax+Ay A=0+Ay A=Ay
What is a vector which is orthogonal to the other vectors and is coplanar with the other vectors called?
In a plane, each vector has only one orthogonal vector (well, two, if you count the negative of one of them). Are you sure you don't mean the normal vector which is orthogonal but outside the plane (in fact, orthogonal to the plane itself)?
What is the definition of orthogonal signal space?
Orthogonal signal space is defined as the set of orthogonal functions, which are complete. In orthogonal vector space any vector can be represented by orthogonal vectors provided they are complete.Thus, in similar manner any signal can be represented by a set of orthogonal functions which are complete.
Which vector combinations cannot be parallel?
Orthogonal ones, for example.
A vedtor which is perpendicular to every vector?
The zero vector is not perpendicular to all vectors, but it is orthogonal to all vectors.
How do you find the y-component of a vector if you are given x-component and z-component?
You don't. Knowing two of the vector's orthogonal components doesn't tell you what the third one is. It could be absolutely anything.
How do you name the direction of a vector?
The direction of a vector is defined in terms of its components along a set of orthogonal vectors (the coordinate axes).
Can a vector with a non zero component be zero?
No. The answer does assume that "components" are defined in the usual sense - that is, a decomposition of the vector along a set of orthogonal axes.
What is the maximun no of components into which a vector can be split?
There is no maximum. A vector can be defined for a hyperspace with any number of dimensions. Such a hyperspace can be described using an orthogonal system of axes and the vector can be split into its components along each one of these axes.
Difference between orthogonal and perpendicular lines?
Orthogonal and perpendicular are essentially the same thing: When two lines, planes, etc. intersect at a right angle, or 90 degrees, they are orthogonal/perpendicular.Orthogonal is simply a term used more commonly for vectors, when they have a scalar/inner/dot product of 0, as:vector u X vector v = (length of vector u) X (length of vector v) X cos @ ,@ being the angle between the two vectors.When the scalar product is 0, that is because @ is 90 degrees, and cos 90 = 0. Therefore, the vectors u and v are orthogonal.
Can a vector have zero magnitude if one of its components is nonzero?
A vector comprises its components, which are orthogonal. If just one of them has magnitude and direction, then the resultant vector has magnitude and direction. Example:- If A is a vector and Ax is zero and Ay is non-zero then, A=Ax+Ay A=0+Ay A=Ay
What does rectangular component of a vector mean?
Any vector can be "decomposed" into components along any two non-parallel directions. In particular, a vector may be decomposed along a pair (more in higher dimensional spaces) of orthogonal directions. Orthogonal means at right angles and so you have the original vector split up into components that are at right angles to each other - for example, along the x-axis and the y-axis. These components are the rectangular components of the original vector. The reason for doing this is that vectors acting at right angles to one another do not affect one another.
Which two trigonometric functions are used for analyzing vectors?
You usually need all three primary functions. The sine and cosine functions are used to resolve the vector along orthogonal axes, and the tangent function is used to find its direction.
