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When simplifying algebra can you simplify 1 over a equals 1 over b to a equals b?
1/a = 1/b: cross multiplying gives a = b
Is the sum of the square of cross and dot products equal to the square of their product?
Your question makes no sense.... What you meant to say is:Is the sum of the square of magnitude of the cross product and the square of dot product of two vectors equal to the product of the square of their magnitudes?i.e:|A x B|2 +(A .B)2 = |A|2|B|2The answer is YES. It is called Lagrange's identity and is a special case of the Binet-Cauchy identity.(Ax B) .(Cx D)+(A.D)(B.C)=(A.C)(B.D)Where A= Cand B= D.
What is the used of dot product and cross product in real life?
The dot-product and cross-product are used in high order physics and math when dealing with matrices or, for example, the properties of an electron (spin, orbit, etc.).
If ax equals b minus cx then x equals?
x = b/(a + c)
A varies directly as b and a equals 12 when b equals 4 What is the constant of variation?
a varies directly as b and a = 12 when b = 4. What is the constant of variation?
When simplifying algebra can you simplify 1 over a equals 1 over b to a equals b?
1/a = 1/b: cross multiplying gives a = b
What is cross-product and dot-product?
Cross products and dot products are two operations that can be done on a pair of 2-dimensional, 3-dimensional, or n-dimensional vectors. Both can be viewed in terms of mathematics or their physical representations.The dot product of two three-dimensional vectors A= and B= is a1b1+ a2b2 + a3b3. The definition in high dimensions is completely analogous. Notice that the dot product of two vectors is a scalar, not a vector. The dot product also equals |A|*|B|cosθ, where |A| and |B| are the magnitudes of A and B, respectively and θ is the angle between the vectors. This is the same as saying that the dot product is the magnitude of one vector multiplied times the component of the second vector that is parallel to the first. Notice that this means that the dot product of two vectors is 0 if and only if they are perpendicular.The cross product is a little more complicated. In three dimensions, A × B = . Notice that this operation results in another vector. This vector always points in a direction perpendicular to both A and B, and this direction can be determined by the right-hand rule. Physically, the magnitude of this vector equals |A|*|B|sinθ, or the magnitude of the first vector times the component of the other that is perpendicular to the first. So the cross product is 0 when the vectors are parallel.
What is the difference between the ''dot product'' and the ''cross product''?
Dot Product:Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.a ● b = ║a║║b║cos(θ)Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and b define.a X b = ║a║║b║sin(θ)n
What is the difference between a 'dot product' and a 'cross product'?
Dot Product:Given two vectors, a and b, their dot product, represented as a ● b, is equal to their magnitudes multiplied by the cosine of the angle between them, θ, and is a scalar value.a ● b = ║a║║b║cos(θ)Cross Product:Given two vectors, a and b, their cross product, which is a vector, is represented as a X b and is equal to their magnitudes multiplied by the sine of the angle between them, θ, and then multiplied by a unit vector, n, which points perpendicularly away, via the right-hand rule, from the plane that a and bdefine.a X b= ║a║║b║sin(θ)n
Dot product of two vectors is equal to cross product what will be angle between them?
(A1) The dot product of two vectors is a scalar and the cross product is a vector? ================================== (A2) The cross product of two vectors, A and B, would be [a*b*sin(alpha)]C, where a = |A|; b = |B|; c = |C|; and C is vector that is orthogonal to A and B and oriented according to the right-hand rule (see the related link). The dot product of the two vectors, A and B, would be [a*b*cos(alpha)]. For [a*b*sin(alpha)]C to equal to [a*b*cos(alpha)], we have to have a trivial solution -- alpha = 0 and either a or b be zero, so that both expressions are zeroes but equal. ================================== Of course one is the number zero( scalar), and one is the zero vector. It is a small difference but worth mentioning. That is is to say if a or b is the zero vector, then a dot b must equal zero as a scalar. And similarly the cross product of any vector and the zero vector is the zero vector. (A3) The magnitude of the dot product is equal to the magnitude of the cross product when the angle between the vectors is 45 degrees.
What are the applications of cross product and dot product in physics?
cross: torque dot: work
When cross and dot product equal what is angle between A and B?
A · B = |A| |B| cos(Θ)A x B = |A| |B| sin(Θ)If [ A · B = A x B ] then cos(Θ) = sin(Θ).Θ = 45°
What would you suggest when A crossB equals 0 and AB equals 0?
Assuming that cross means 'divide' B is equal to 0
What is the cross of a 't' and a dot of an 'I' called?
The dot of an 'i' is called a tittle and the cross of a 't' is called a T-bar.
Who is the commutative property in dot and cross product?
The cross product results in a vector quantity that follows a right hand set of vectors; commuting the first two vectors results in a vector that is the negative of the uncommuted result, ie A x B = - B x A The dot product results in a scalar quantity; its calculation involves scalar (ie normal) multiplication and is unaffected by commutation of the vectors, ie A . B = B . A
What is the cross product method?
If a is to b as c is to d, a x d = b x c. The product of the means (b & c) equals the product of the extremes (a & d).
Is the sum of the square of cross and dot products equal to the square of their product?
Your question makes no sense.... What you meant to say is:Is the sum of the square of magnitude of the cross product and the square of dot product of two vectors equal to the product of the square of their magnitudes?i.e:|A x B|2 +(A .B)2 = |A|2|B|2The answer is YES. It is called Lagrange's identity and is a special case of the Binet-Cauchy identity.(Ax B) .(Cx D)+(A.D)(B.C)=(A.C)(B.D)Where A= Cand B= D.
