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What is the formula for calculating the resultant of two vectors of same magnitude and how?
Wiki User
∙ 12y ago
Divide each vector into components, that is, find components in the x, y and z direction that add up to give the vector. This requires some basic trigonometry. Then, add the the components.
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In 2-d the answer is as follows:
Suppose the two vectors have magnitude R and are angles A and B to the x-axis.
Therefore, the horizontal components of the two vectors are RcosA and RcosB
so that the resultant has horizontal component RcosA + RcosB
XR = 2R*cos[(A+B)/2]*cos[(A-B)/2]
The vertical components of the original two vectors are RsinA and RsinB
so that the resultant has horizontal component RsinA + RsinB
YR = 2R*sin[(A+B)/2]*cos[(A-B)/2]
From these two equations, the magnitude of the resultant is
sqrt(XR2 + YR2) = sqrt{4R2*cos2[(A-B)/2]} = 2R*cos[(A-B)/2]
and the direction of the resultant is
arctan(YR/XR) = arctan{[(A+B)/2]} = (A+B)/2 or equivalent
Wiki User
∙ 12y ago
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What should be the angle between two vectors of magnitudes 8 and 8 units so that their resultant has a magnitude of 20 units?
It is not possible. The maximum magnitude is obtained when the vectors are aligned and in this case the resultant has a magnitude which is the sum of the individual vectors. In the given example, the maximum possible magnitude for the resultant is 16 units. In general |a+b| <= |a| + |b| where a, b are vectors and |a| is the magnitude of a
Can the magnitude of resultant of two vectors of the same magnitude be equal of magnitude of either vector?
yes
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vector proof mathematically?
Yes. If the two vectors are two sides of an equilateral triangle, then the resultant is the third side and therefore equal in magnitude.
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vector. How?
Yes - if the vectors are at an angle of 60 degrees. In that case, the two vectors, and the resultant, form an equilateral triangle.Yes - if the vectors are at an angle of 60 degrees. In that case, the two vectors, and the resultant, form an equilateral triangle.Yes - if the vectors are at an angle of 60 degrees. In that case, the two vectors, and the resultant, form an equilateral triangle.Yes - if the vectors are at an angle of 60 degrees. In that case, the two vectors, and the resultant, form an equilateral triangle.
What is the magnitude of the resultant of a pair of perpendicular 300 N vectors?
The magnitude depends on the angle between the vectors. The magnitude could be from 0 to 600 N.
What is the formula for calculating magnitude of resultant vector?
The formula for calculating the magnitude of the resultant vector when adding two vectors is: magnitude = sqrt((vector1 magnitude)^2 + (vector2 magnitude)^2 + 2 * vector1 magnitude * vector2 magnitude * cos(theta)) where theta is the angle between the two vectors.
When are magnitudes of 2 vectors added?
The magnitudes of two vectors are added when calculating the resultant magnitude of their vector sum. This can be done using the Pythagorean theorem, where the magnitude of the resultant vector is the square root of the sum of the squares of the magnitudes of the individual vectors.
Can the resultant or two vectors of the same magnitude be equal to the magnitude of either of the vectors?
No, the resultant of two vectors of the same magnitude cannot be equal to the magnitude of either of the vectors. The magnitude of the resultant of two vectors is given by the formula: magnitude = √(A^2 + B^2 + 2ABcosθ), where A and B are the magnitudes of the vectors and θ is the angle between them.
Can the resultant of two equal vectors be of same magnitude as the two vectors?
No, the resultant of two equal vectors will have a magnitude that is not equal to the magnitude of the original vectors. When two vectors are added together, the resulting vector will have a magnitude that depends on the angle between the two vectors.
When two vectors are added and their magnitude is equal to the magnitude of resultan what will be angle in between them?
The angle between two vectors whose magnitudes add up to be equal to the magnitude of the resultant vector will be 120 degrees. This is known as the "120-degree rule" when adding two vectors of equal magnitude to get a resultant of equal magnitude.
What should be the angle between two vectors of magnitudes 8 and 8 units so that their resultant has a magnitude of 20 units?
It is not possible. The maximum magnitude is obtained when the vectors are aligned and in this case the resultant has a magnitude which is the sum of the individual vectors. In the given example, the maximum possible magnitude for the resultant is 16 units. In general |a+b| <= |a| + |b| where a, b are vectors and |a| is the magnitude of a
How great is the resultant of two equal-magnitude vectors at right angles to each other?
Let two equal magnitude vectors be 'X'.. Then, resultant=1.414X
What is the magnitude of the two vectors having a sum of zero?
If their sum (resultant) is 0, then the magnitude of the resultant must be 0.
Two vectors of unequal magnitude can their sum be zero?
No, two vectors of unequal magnitude cannot have a sum of zero. The resultant of adding two vectors is determined both by their magnitudes and directions. If the vectors have unequal magnitudes, the resultant vector will have a magnitude that is at least as large as the larger of the two original vectors.
Can the magnitude of resultant of two vectors of the same magnitude be equal of magnitude of either vector?
yes
What is the magnitude of the resultant vectors when the angle between them is 60 degrees?
To find the magnitude of the resultant vectors when the angle between them is 60 degrees, you can use the formula for finding the resultant of two vectors: magnitude of R = sqrt(A^2 + B^2 + 2AB*cos(theta)), where A and B are the magnitudes of the two vectors and theta is the angle between them. Plug in the values of A, B, and theta to calculate the magnitude of the resultant vector.
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vector proof mathematically?
Yes. If the two vectors are two sides of an equilateral triangle, then the resultant is the third side and therefore equal in magnitude.
