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.
decomposition of a vector into its components is called resolution of 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
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.
reverse process of vector addition is vector resolution.
Vector spaces can be formed of vector subspaces.
Resultant vector or effective vector
decomposition of a vector into its components is called resolution of vector
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.
A scalar times a vector is a vector.
No, magnitude is not a vector. Magnitude refers to the size or quantity of a vector, but it does not have direction like a vector does.
The vector obtained by dividing a vector by its magnitude is called a unit vector. Unit vectors have a magnitude of 1 and represent only the direction of the original vector.