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What property shows ab equals ab?
Identity
What is scalar and vector product?
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.
Is ray AB always the same as ray BA?
Yes, provided it is the ray. If AB is a vector then the answer is no.
What is AC-BC equals AB?
It could be a vector sum.
How do you find the dot product ab of two vectors if you know their lengths and the angle between them?
<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.
What property shows ab equals ab?
Identity
What is scalar and vector product?
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.
Is ray AB always the same as ray BA?
Yes, provided it is the ray. If AB is a vector then the answer is no.
What is AC-BC equals AB?
It could be a vector sum.
How do you find the dot product ab of two vectors if you know their lengths and the angle between them?
<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.
Does 4d exist?
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.
1 For the two vectors find the scalar product AB and the vector product?
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.
Will a vector multiplied by another vector result in another vector?
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.
What is the form of the sum of cubes identity?
a3 + b3 = (a + b)*(a2 - ab + b2)anda3 - b3 = (a - b)*(a2 + ab + b2)
What are the properties of a group?
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.
which is the component form of AB?
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).
How do you calculate magnitude and direction of a resultant vector by parallelogram law?
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.
