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
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
yes
Yes. If the two vectors are two sides of an equilateral triangle, then the resultant is the third side and therefore equal in magnitude.
The magnitude depends on the angle between the vectors. The magnitude could be from 0 to 600 N.
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.
|v| = vx|v| = Sqrt(vx2 + vy2)|v| = Sqrt(vx2 + vy2 + vz2)
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
Let two equal magnitude vectors be 'X'.. Then, resultant=1.414X
If their sum (resultant) is 0, then the magnitude of the resultant must be 0.
yes
Yes. If the two vectors are two sides of an equilateral triangle, then the resultant is the third side and therefore equal in magnitude.
if you add the vectors magnitude and equal to resultant the angle between them is 0
The magnitude depends on the angle between the vectors. The magnitude could be from 0 to 600 N.
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.
Yes.
Magnitude? Yes. Simple answer: think of it as a triangle. Can a triangle have three sides of the same length? Yes. Long answer: there really isn't a long answer. To get the resultant of two vectors, one would add up the components of each vector. While it is impossible to add two vectors of the same magnitude and derive a resultant of the same magnitude AND DIRECTION as one of the vectors, one need only to create a directional difference of exactly 60 degrees between the first two vectors to result in a resultant of like magnitude. Math really is the most perfect language. Vectors are to triangles what optics are to to the study of conics!
at 120 degree