Identity
Yes, provided it is the ray. If AB is a vector then the answer is no.
The scalar product of two vectors, A and B, is a number, which is a * b * cos(alpha), where a = |A|; b = |B|; and alpha = the angle between A and B. The vector product of two vectors, A and B, is a vector, which is a * b * sin(alpha) *C, where C is unit vector orthogonal to both A and B and follows the right-hand rule (see the related link). ============================ The scalar AND vector product are the result of the multiplication of two vectors: AB = -A.B + AxB = -|AB|cos(AB) + |AB|sin(AB)UC where UC is the unit vector perpendicular to both A and B.
It could be a vector sum.
<ab> = |a|*|b|*cos(x) where |a| is the length of the vector a, |b| is the length of the vector b, and x is the angle between them.
Identity
Yes, provided it is the ray. If AB is a vector then the answer is no.
The scalar product of two vectors, A and B, is a number, which is a * b * cos(alpha), where a = |A|; b = |B|; and alpha = the angle between A and B. The vector product of two vectors, A and B, is a vector, which is a * b * sin(alpha) *C, where C is unit vector orthogonal to both A and B and follows the right-hand rule (see the related link). ============================ The scalar AND vector product are the result of the multiplication of two vectors: AB = -A.B + AxB = -|AB|cos(AB) + |AB|sin(AB)UC where UC is the unit vector perpendicular to both A and B.
It could be a vector sum.
<ab> = |a|*|b|*cos(x) where |a| is the length of the vector a, |b| is the length of the vector b, and x is the angle between them.
In mathematics and physics, we commonly work in four-dimensional space-time. This includes the three spatial dimensions (length, width, height) and time as the fourth dimension. However, in our everyday experience, we can only perceive and navigate in three spatial dimensions.
For two vectors A and B, the scalar product is A.B= -ABcos(AB), the minus sign indicates the vectors are in the same direction when angle (AB)=0; the vector product is ABsin(AB). Vectors have the rule: i^2= j^2=k^2 = ijk= -1.
It depends on the angle between the vectors (AB). The product of two vectors Av and Bv is AvBv=-Av.Bv + AvxBv= |AvBv|(-cos(Ab) + vsin(AB)). If the angle is a odd multiple of 90 degrees the product is a vector. If he angle is an even multiple of 90 degrees, the product is a scalar. If he angle is not a multiple of 90 degrees, the product of a vector by another vector is a quaternion, the sum of a scalar and a vector. Most numbers in physics and science are quaternions, a combination of scalars and vectors.Quaternions forma mathematical Group, vectors don't. The product of quaternions is always a quaternion. The product of vectors may not be a vector, it may be a vector , a scalar or both. The product of scalars is also a Group. Vector by themselves do not form a Group. The Order of Numbers are Scalars form a Group called Real Numbers; scalars and a single vector form a group called complex numbers; scalars and three vectors form a group called Quaternions. These are the only Groups that provide an Associative Division Algebra.
a3 + b3 = (a + b)*(a2 - ab + b2)anda3 - b3 = (a - b)*(a2 + ab + b2)
In abstract algebra, the properties of a group G under a certain operation are:Associativity: (ab)c = a(bc) for all a, b and c belonging to GIdentity: Identity e belongs to G.Inverse: If ab = ba = a, where a is the identity, then b is the inverse of a.
The component form of a vector AB would typically be represented as (x2 - x1, y2 - y1), where A is at the point (x1, y1) and B is at the point (x2, y2).
To find the resultant of 2 vectors, P and Q, let the ray AB represent the vector P. Let AB (not BA) be in the direction of P and let the length of AB represent the magnitude of P. Let BC represent the direction of Q and the length BC represent the magnitude of Q [on the same scale used for P and AB]. Then the straight line AC, which is the diagonal of the parallelogram with sides representing P and Q, is the resultant vector R, with magnitude and direction represented by AC.The vectors P and Q can also be represented as sides AB and AC. In that case you will need to complete the parallelogram and the resultant is represented by the diagonal through A.