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Then, if A nd B are scalars, it is not really surprising. If A and B are vectors then they have the same direction.
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Prove that two vectors must have equal magnitude if their sum is perpendicular to their difference?
Suppose the condition stated in this problem holds for the two vectors a and b. If the sum a+b is perpendicular to the difference a-b then the dot product of these two vectors is zero: (a + b) · (a - b) = 0 Use the distributive property of the dot product to expand the left side of this equation. We get: a · a - a · b + b · a - b · b But the dot product of a vector with itself gives the magnitude squared: a · a = a2 x + a2 y + a2 z = a2 (likewise b · b = b2) and the dot product is commutative: a · b = b · a. Using these facts, we then have a2 - a · b + a · b + b2 = 0 , which gives: a2 - b2 = 0 =) a2 = b2 Since the magnitude of a vector must be a positive number, this implies a = b and so vectors a and b have the same magnitude.
What is the algebraic expression for ten more than the product of a and b?
It is: ab+10
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 ab times b?
(a x b)^b =ab x b^2 =ab^3
What is the equation of ab?
a+b(a+B)=ab
Why is scalar product two vectors a scalar?
Scalar product of two vectors is a scalar as it involves only the magnitude of the two vectors multiplied by the cosine of the angle between the vectors.
When is the magnitude of A plus B equal to the magnitude of A B?
a + b = ab a = ab - b = b(a - 1) b = a / (a-1) Any pair of numbers that satisfy that equation, e.g. a = 3, b = 1½ . . . because 3 + 1½ = 4½ and 3 x 1½ = 4½ another example: a = 101, b = 1.01 because 101 + 1.01 = 102.01, and 101 x 1.01 = 102.01
Twice the product of a and b?
x=ab
How to find the area of a parallelogram with given vertices's in a 3D figure?
You need to take the magnitude of the cross-product of two position vectors. For example, if you had points A, B, C, and D, you could take the cross product of AB and BC, and then take the magnitude of the resultant vector.
What is A over B equal to?
AB
How do you determine the magnitude and the direction of the resultant of nonconcurrent forces?
The resultant (sum) of nonconcurrent forces is given by the Law of Cosines, which is the product of the vector sums and their conjugate: C^2 = (A + B)(A + B)*=(AA* + BB* + AB* + A*B)= (AA* + BB* + 2ABcos(AB)) The angle of C is given by sin (C) =A/C sin(AB) angle(C ) is smaller than the angle between A and B, angle(AB).
What is the product of -a and -b?
Negative times negative equals positve, so -a*-b=ab (positive ab)
What does ab equals 1a plus 1B plus ab equal to?
ab=1a+1b a is equal to either 0 or two, and b is equal to a
What is the value of scalar product of two vectors A and B where value of vector A and B is not zero and vector product of two vectors A and B is not zero?
Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')
Why does b times ab equal ab squared and not equal ab plus b squared?
b*ab = ab2 Suppose b*ab = ab + b2. Assume a and b are non-zero integers. Then ab2 = ab + b2 b = 1 + b/a would have to be true for all b. Counter-example: b = 2; a = 3 b(ab) = 2(3)(2) = 12 = ab2 = (4)(3) ab + b2 = (2)(3) + (2) = 10 but 10 does not = 12. Contradiction. So it cannot be the case that b = 1 + b/a is true for all b and, therefore, b*ab does not = ab + b2
Two fractions whose product is 1 are known as?
Reciprocals. Example (a/b)(b/a)=(ab/ab)=1
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.
