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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.
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Can a vector be represented in terms of unit 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.
Is vector A parallel vector B given that vector A is equal to the zero vector and vector B is equal to the zero 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.
Vector that shows the combined effect of two or more vector?
Resultant vector or effective vector
What is relationship between vector space and vector subspace?
Vector spaces can be formed of vector subspaces.
What is different between negative vector and null 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.
Can a vector be represented in terms of unit 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.
What is null 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...
What is the angle between vector a and vector b when mode of vector a plus vector b is equal to mode of vector a minus vector b?
90 degrees
Is vector A parallel vector B given that vector A is equal to the zero vector and vector B is equal to the zero 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.
What is the reverse process of vectors addition?
reverse process of vector addition is vector resolution.
What is relationship between vector space and vector subspace?
Vector spaces can be formed of vector subspaces.
Vector that shows the combined effect of two or more vector?
Resultant vector or effective vector
What is different between negative vector and null 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.
What is resolution of vector?
Spliting up of vector into its rectangular components is called resolution of vector
What is a scalar times a vector?
A scalar times a vector is a vector.
What is the physical significance of null vectors?
Zero vector or null vector is a vector which has zero magnitude and an arbitrary direction. It is represented by . If a vector is multiplied by zero, the result is a zero vector. It is important to note that we cannot take the above result to be a number, the result has to be a vector and here lies the importance of the zero or null vector. The physical meaning of can be understood from the following examples. The position vector of the origin of the coordinate axes is a zero vector. The displacement of a stationary particle from time t to time tl is zero. The displacement of a ball thrown up and received back by the thrower is a zero vector. The velocity vector of a stationary body is a zero vector. The acceleration vector of a body in uniform motion is a zero vector. When a zero vector is added to another vector , the result is the vector only. Similarly, when a zero vector is subtracted from a vector , the result is the vector . When a zero vector is multiplied by a non-zero scalar, the result is a zero vector.
If a vector quantity is divided by its magnitude the vector obtained is called?
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.
