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Q: When magnitude of vector a plus b is equal to the magnitude of vector a minus b then what is the angle between two vectors a and b?

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That fact alone doesn't tell you much about the original two vectors. It only says that (magnitude of vector-#1) times (magnitude of vector-#2) times (cosine of the angle between them) = 1. You still don't know the magnitude of either vector, or the angle between them.

69 degrees

iff the angle between them is 120 degrees

When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in thesame direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.

7

Depends on the situation. Vector A x Vector B= 0 when the sine of the angle between them is 0 Vector A . Vector B= 0 when the cosine of the angle between them is 0 Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.

if you add the vectors magnitude and equal to resultant the angle between them is 0

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.

Scalar product = (magnitude of 'A') times (magnitude of 'B') times (cosine of the angle between 'A' and 'B')

If the angle decreases, the magnitude of the resultant vector increases.

using the "dot product" formula, you can find the angle. where |a| denotes the length (magnitude) of a. More generally, if b is another vector : where |a| and |b| denote the length of a and b and θis the angle between them. Thus, given two vectors, the angle between them can be found by rearranging the above formula: : :

When the angle between any two component vectors is either zero or 180 degrees.

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