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69 degrees

Q: What is the angle between two vectors of equal magnitude whose resultant is equal to the magnitude of either vector?

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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.

120 deg

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!

Yes. As an extreme example, if you add two vectors of the same magnitude, which point in the opposite direction, you get a vector of magnitude zero as a result.

Related questions

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.

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.

120 deg

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!

Yes. As an extreme example, if you add two vectors of the same magnitude, which point in the opposite direction, you get a vector of magnitude zero as a result.

Yes. Imagine an equilateral triangle. If two vectors are in the directions - and lengths - of two of the sides, the resultant will be the third side (depending on the directions chosen, of course).

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.

If the directions of two vectors with equal magnitudes differ by 120 degrees, then the magnitude of their sum is equal to the magnitude of either vector.

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.

Yes, the magnitude of the difference between two vectors can be greater than the magnitude of either vector. This can occur when the vectors are in opposite directions or have different magnitudes such that the resulting difference vector is longer than either of the original vectors.

No, the statement is incorrect. The sum of two vectors of equal magnitude will not equal the magnitude of either vector. The sum of two vectors of equal magnitude will result in a new vector that is larger than the original vectors due to vector addition. The magnitude of the difference between the two vectors will be smaller than the magnitude of either vector.