What is the square of the sum of two vectors?

The resultant of two vectors acting at right angles to each other is equal to the square root of the sum of the squares of the magnitudes of the two vectors. Direction of the resultant depends upon their relative magnitudes.

Can the sum of two vectors of equal magnitude be equal to magnitude of either of the vectors?

If you add two vectors with equal magnitude, and the magnitude of the resultant vector is equal to the magnitude of both vectors, then the three vectors obviously form an equilateral triangle. As @almagest said, this means that the difference between the angles of the two vectors is 120 degrees.

Under what conditions would the sum of the magnitudes of the vectors equal the magnitude of the resultant vector?

A:The sum and difference of two vectors will be equal in magnitude when two vectors are perpendicular to each other. B:The sum and difference of two vectors will have the same direction, when the vectors have unequal magnitudes but are in the same direction.

What is the norm of the sum of two vectors?

Norm of a vector obeys triangular inequality that the norm of a sum of two vectors is less than or equal to the sum of the norms ‖ a + b ‖ ⩽ ‖ a ‖ + ‖ b ‖ .

How can vectors be added?

To add vectors, merely express both of them in terms of their horizontal and vertical components and then add the components together. This can be seen by adding the horizontal components of the two vectors (4+4 ) and the two vertical components (3+3 ).

How can the magnitude of resultant of two equal vectors be equal to each of them?

120° Hint: It is given that two vectors are equal in magnitude i.e. if A and B are two vectors then ∣A∣=∣B∣. It is also mentioned that the magnitude of resultant is equal to the magnitude of either of them i.e. ∣A∣=∣B∣=∣A+B∣.

How do you add magnitude of two vectors?

To add the two vectors, add them in coordinate form: (3.5, 3.5) + (5.7, 4.0) = (9.2, 7.5). Convert (9.2, 7.5) into magnitude/angle form. Apply the equation theta = tan–1(y/x) to find the angle, which is tan–1(7.5/9.2) = tan–1(0.82) = 39 degrees. Converting to two significant digits gives you 12.

What is the magnitude of the sum of the first two vectors?

Hence the magnitude of the sum vector of the first two vectors must equal either one of them as well. only imagine that the top angles are 120 degrees, and the bottom angles ar e60 degrees.] Now if you mean that the actual vectors are identical, magnitude and direction, then only the trivial null case applies.

How do you find the sum of three equal vectors?

Thus the three vectors are equally distributed over 360 degrees and by symmetry must cancel to zero. If so, the sum of the first two vectors may replace them, and again by symmetry, the sum vector must be positioned exactly midway between them, and diametrically opposite the third vector. Hence these two must have equal magnitude, c

Can two vectors of the same magnitude have the same angle?

Yes it is possible, if only the magnitudes of the 2 vectors are equal. of the same magnitude v makes an angle of 120 ∘ with the first vector. Yes it is possible, if only the magnitudes of the 2 vectors are equal. of the same magnitude v makes an angle of 120 ∘ with the first vector.

When vectors A and B are opposite to each other?

Its given magnitude of sum of vectors is equal to the difference of their magnitudes. Which means for @= 180°. This case is possible. So, when vectors A and B are opposite to each other their magnitude of sum and difference of magnitudes are equal. P.S. – Sorry for reading the question wrong.