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What property shows ab equals ab?
Identity
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 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.
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
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 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.
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?
Yes! There is one real (distance) dimension r=ct and three vector (displacement) dimensions called vectors ,V=Ix + Jy + Kz. Together they make up a 4D space called Quaternions [r,V] = [r, ix +Jy + Kz]. The Cosmos consists of these Quaternions. Most variables in Physics are Quaternions consisting of a real (small letter) and a vector (Capital letter) .e.g. [a,A] Consider two Quaternions [a,A] and [b.B] Addition: [a,A] + [b,B] = [a +b, A +B] Multiplication: [a,A] [b,B] = [ab -A.B, aB + Ab + AxB] Multiplication includes Complex Number multiplication. A.B indicates vector parallel product |AB|cos(AB) and A.B=0 if the vectors A and B are perpendicular,e.g I.J=0. AxB indicates vector perpendicular product |AB|sin(AB) and AxB=0 if the vectors A and B are parallel, e.g IxI=0. Complex Numbers are two dimensional and only have one vector I, C=[a,ib] where 'i' indicates the singular vector. Quaternions contain the real numbers and the Complex Numbers as subsets of the 4D Quaternions. The three dimensions of space are vector dimensions and the real dimension is r=ct. Mathematically, the real dimension is critical to making mathematics and Physics work.
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 is the law of moment?
forces whose lines of action meet at a common pointexplanation-consider two forces p and q acting at a point a...let ab vector and ac vector represent p and q in magnitude and direction.then according to law of parallelogram of forces,diagnol ad represents in magnitude and drection the resultant r and p and q i.e,ab vector+ac vector=ad vector
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.
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.
