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The sum of two vectors is a minimum when the angle between them is what?
Wiki User
∙ 14y ago
180 degrees. Then the sum of the two vectors has a magnitude
equal to the difference of their individual magnitudes.
Wiki User
∙ 14y ago
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What is the angle between two vectors if their sum is to be maximum?
The resultant vector has maximum magnitude if the vectors act in concert. That is, if the angle between them is 0 radians (or degrees). The magnitude of the resultant is the sum of the magnitudes of the vectors.For two vectors, the resultant is a minimum if the vectors act in opposition, that is the angle between them is pi radians (180 degrees). In this case the resultant has a magnitude that is equal to the difference between the two vectors' magnitudes, and it acts in the direction of the larger vector.At all other angles, the resultant vector has intermediate magnitudes.
When is the vector sum equal in magnitude to the algebraic sum?
When the angle between any two component vectors is either zero or 180 degrees.
Can the sum of two vectors be a scalar?
No.
How can you use the pythagorean theorem to add two vectors that are perpindicular to each other?
Construct the rectangle that contains the right angle subtended by the vectors. Calculate or construct the diagonal of the rectangle. The diagonal is the hypotenuse of a right triangle with the two vectors as sides. The hypotenuse is also the vector that is the sum of the two original vectors. Calculate the magnitude of that vector by applying the theorem.
Can the directions of the sum of two two vectors be equal to the directions of difference of two vectors?
Yes.
When the angle between two vectors is equal to zero?
When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in thesame direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.
What is the angle between two vectors when their sum is maximum?
00
What is the angle between 2 vectors when their sum is maximum?
180 degrees* * * * *The exact opposite!Maximum = 0 degrees, minimum = 180 degrees.
What is the angle between two vectors if their sum is to be maximum?
The resultant vector has maximum magnitude if the vectors act in concert. That is, if the angle between them is 0 radians (or degrees). The magnitude of the resultant is the sum of the magnitudes of the vectors.For two vectors, the resultant is a minimum if the vectors act in opposition, that is the angle between them is pi radians (180 degrees). In this case the resultant has a magnitude that is equal to the difference between the two vectors' magnitudes, and it acts in the direction of the larger vector.At all other angles, the resultant vector has intermediate magnitudes.
How angle between vectors affects the resultant?
The Law of Cosines shows the affect of the angle between vectors. R^2 = (A+B)(A +B)*= (AA* + BB* + 2ABcos(AB)) If the angle is less than 90 degrees the resultant squared R^2 is greater than the sum of the vectors squared. If the angle is 90 degrees the resultant squared is the sum of the vectors squared. If the angle is greater than 90 degrees, the resultant squared is less than the Sum of the vectors squared.
What is the angle between the two vectors if their sum has a magnitude of 2F?
We can't answer that without also knowing the magnitude of the individual vectors.
What is the minimum number of vectors with equal magnitudes whose vector sum can be zero?
Two is the minimum number of vectors that will sum to zero.
What are the conditions for maximum and minimum sum or resultant of two vectors?
We have 2 vectors: AC, BD. Then |AC| = a and |BD|=b (i want to make it easier) and sum i'll call s , where s = AC + BD (we're adding vectors) there is an equation: s2 = a2 + b2 - 2ab cos x , where x is an angle between vectors a and b. The sum has a maximum value when x = 0 and the minimum value when x=180*=pi (rad)
When is the vector sum equal in magnitude to the algebraic sum?
When the angle between any two component vectors is either zero or 180 degrees.
Can the sum of magnitudes of two vectors ever be equal to the magnitude of the sum of these two vectors?
Sure, if the two vectors point in the same direction.When we need the sum of magnitudes of two vectors we simply add the magnitudes, but to get the magnitude of the sum of these two vectors we need to add the vectors geometrically.Formula to find magnitude of the sum of these two vectors is sqrt[ |A|2 +|B|2 +2*|A|*|B|*cos(z) ] where |A| and |B| are magnitudes of two A and B vectors, and z is the angle between the two vectors.Clearly, magnitude of sum of two vectors is less than sum of magnitudes(|A| + |B|) for all cases except when cos(z)=1(for which it becomes = |A| + |B| ). Cos(z)=1 when z=0, i.e. the vectors are in the same direction(angle between them is 0).Also if we consider addition of two null vectors then their sum is zero in both ways of addition.So, we get two caseswhen the two vectors are in same direction, andwhen the two vectors are null vectors.In all other cases sum of magnitudes is greater than magnitude of the sum of two vectors.
What is the angle needed for the smallest resultant of two vectors?
The smallest resultant of two vectors is the sum of two equal vectors which make an angle of 180 degrees among each other.
Is the sum of two vectors of equal magnitude equal to the magnitude of either vectors AND their difference root 3 times the magnitude of each vector?
iff the angle between them is 120 degrees
