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Vectors add at rightangle bythe pythagoran theorem: resultant sum = square root of (vector 1 squared + vector 2 squared)

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Q: When adding two vectors at right angles is the resultant of the vectors the algebraic sum of the two vectors?

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If both vectors are of the same magnitude, and the resultant is equal to one, then all three are equal. This describes an equilateral triangle.Since the angles of a triangle must sum to 180, the three angles of an equilateral triangle are all 60 degrees.

A touch over 7. More exactly 7.0711.

yes, if they are at right angles to each other.

If two vectors with equal magnitudes 'M' have perpendicular directions, then the resultant ismidway between them ... 45 degrees from each ... and the magnitude of the resultant isM sqrt(2).84 km/hr North + 84 km/hr East = 84 sqrt(2) = 118.794 km/hr Northeast (rounded).

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. * * * * * 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

Related questions

Let two equal magnitude vectors be 'X'.. Then, resultant=1.414X

When you resolve a vector, you replace it with two component vectors, usually at right angles to each other. The resultant is a single vector which has the same effect as a set of vectors. In a sense, resolution and resultant are like opposites.

A triangle...

The outcome is called the resultant no matter what angle At right angles the resultant is calculated a the hypotenuse of the triangle with each vector as sides

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.

If both vectors are of the same magnitude, and the resultant is equal to one, then all three are equal. This describes an equilateral triangle.Since the angles of a triangle must sum to 180, the three angles of an equilateral triangle are all 60 degrees.

A touch over 7. More exactly 7.0711.

yes, if they are at right angles to each other.

If two vectors with equal magnitudes 'M' have perpendicular directions, then the resultant ismidway between them ... 45 degrees from each ... and the magnitude of the resultant isM sqrt(2).84 km/hr North + 84 km/hr East = 84 sqrt(2) = 118.794 km/hr Northeast (rounded).

Small angles are NOT called vectors. The question appears to be based on some misunderstanding.

No matter what the angles are:* Express the vectors in Cartesian (rectangular) coordinates; in two dimensions, this would usually mean separating them into an x-component and a y-component. * Add the components of all the vectors. For example, the x-component of the resultant vector will be the sum of the x-components of all the other vectors. * If you so wish (or the teacher so wishes!), convert the resulting vector back into polar coordinates (i.e., distance and direction).

vectors or lines