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 vector orthogonal to other vectors in the plane is called the normal vector
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'.
The zero vector is not perpendicular to all vectors, but it is orthogonal to all vectors.
In geometry a vector is used to make the equations easier to understand and to figure out. Velocity and force are examples of vectors. For a vector to be coplanar there must be two or more and they must be linearly dependent. Coplanar vectors have proportional components and their rank is 2.
The direction of a vector is defined in terms of its components along a set of orthogonal vectors (the coordinate axes).
Easy, the fourth vector (D) be opposite the sum of the other three non-coplanar vectors (A , B, C). 0=A + B + C + D where D = -(A + B + C).
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'.
Coplanar vectors are vectors lying in the same plane.
The zero vector is not perpendicular to all vectors, but it is orthogonal to all vectors.
In geometry a vector is used to make the equations easier to understand and to figure out. Velocity and force are examples of vectors. For a vector to be coplanar there must be two or more and they must be linearly dependent. Coplanar vectors have proportional components and their rank is 2.
Three vectors sum to zero under the condition that they are coplanar (lie in a common plane) and form a triangle. If the vectors are not coplanar, they will not sum to zero. Another way of looking at it is that the sum is zero if any vector is exactly equal in magnitude and opposite in direction to the vector sum (so-called resultant) of the remaining two.
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.
The direction of a vector is defined in terms of its components along a set of orthogonal vectors (the coordinate axes).
Easy, the fourth vector (D) be opposite the sum of the other three non-coplanar vectors (A , B, C). 0=A + B + C + D where D = -(A + B + C).
The magnitude of a vector is 0 if the magnitude is given to be 0.The magnitude of the resultant of several vectors in n-dimensional space is 0 if and only if the components of the vectors sum to 0 in each of a sewt of n orthogonal directions.
Vector addition does not follow the familiar rules of addition as applied to addition of numbers. However, if vectors are resolved into their components, the rules of addition do apply for these components. There is a further advantage when vectors are resolved along orthogonal (mutually perpendicular) directions. A vector has no effect in a direction perpendicular to its own direction.
A resultant Vector.
The orientation of the three vectors that sum to zero must be coplanar, contained in the same common plane, including being contained in a common line in a plane.