A vector is a part of a more general number or quantity, called a Matrix or Quaternion.
Vectors were developed by William Rowan Hamilton as part of a Quaternion. The Quaternion consists of a scalar part 1 and three vectors I ,J and K.. The scalar is a real number and InJ and K are vector numbers, where I^2 = J^2 = K^2 = -1.. Vectors denote directions such as an axis in space, Ix + Jy + Kz.
Quaternions Q = s + V = Q(cos(Q) + Vsin(Q)) = [cos(Q), sin(Q)(I + J + K)] .
The Quaternion is vector if the angle is an even multiple 90 degrees and the Quaternion is a vector when the angle is a odd multiple of 90 degrees.. If the angle is not a multiple of 90 degrees, the Quaternion is part scalar and part vector. Most variables in physics are Quaternions.
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A 'vector' quantity is a quantity that has both a size and a direction.
Examples are: force, velocity, acceleration, and electric field.
A 'scalar' quantity is a quantity that has size but no direction.
Examples are: cost, temperature, speed, and volume.
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
Resultant vector or effective vector
Vector spaces can be formed of vector subspaces.
A null vector has no magnitude, a negative vector does have a magnitude but it is in the direction opposite to that of the reference vector.
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
NULL VECTOR::::null vector is avector of zero magnitude and arbitrary direction the sum of a vector and its negative vector is a null vector...
90 degrees
That is usually called the resultant vector.
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
It is a displacement vector.
Resultant vector or effective vector
Vector spaces can be formed of vector subspaces.
A null vector has no magnitude, a negative vector does have a magnitude but it is in the direction opposite to that of the reference vector.
Spliting up of vector into its rectangular components is called resolution of vector
A scalar times a vector is a vector.
Vector addition derives a new vector from two or more vectors, and vector resolution is breaking a vector down into its two or more components.