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Can the magnitude of the sum of two two vectors be equal to the magnitude of difference of two vectors?
Yes, this happens if and only if the two vectors are perperndicular:
Since the magnitudes are always positive we can WLOG equate their squares instead:
|a+b|^2 = (a+b)(a+b) = AA + 2ab + bb
|a-b|^2 = (a-b)(a-b) = AA - 2ab + bb
Which are equal iff ab = 0. So for instance take (1,0) and (0,1) as your two vectors and behold: |(1,1)| = |(1,-1)|.
What else can I help you with?
When is the sum of the magnitudes of two vectors equal to the magnitude of the sum of the vectors?
When the vectors are parallel, i.e. both have the same direction.
Can the sum of two equal vectors be equal to either of the vectors?
Only if one of them has a magnitude of zero, so, effectively, no.
When Two vectors have unequal magnitude can their sum be zero explain reason?
No two vectors of unequal magnitude cannot give the sum 0 because for 0 sum the 2 vectors must be equal and in opposite direction
Can the sum of the magnitudes of two vectors ever b equal to the the sum of these two vectors?
Not really. The sum of the magnitudes is a scalar, not a vector - so they can't be equal. But the sum of the two vectors can have the same magnitude, if both vectors point in the same direction.
Is it is possible to add three vectors of equal magnitude and get zero?
Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.
Is the sum of two vectors of equal magnitude equal to the magnitude of either vectors AND their difference root 3 times the magnitude of each vector?
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.
The sum of two vectors is a minimum when the angle between them is what?
180 degrees. Then the sum of the two vectors has a magnitude equal to the difference of their individual magnitudes.
When is the vector sum not equal in magnitude to the algebraic sum?
The magnitude of the vector sum will only equal the magnitude of algebraic sum, when the vectors are pointing in the same direction.
When is the sum of the magnitudes of two vectors equal to the magnitude of the sum of the vectors?
When the vectors are parallel, i.e. both have the same direction.
Can the sum of two equal vectors be equal to either of the vectors?
Only if one of them has a magnitude of zero, so, effectively, no.
Can the sum of two vectors be equal to either of vectors Explain?
No, the sum of two vectors cannot be equal to either of the vectors. Adding two vectors results in a new vector, with a magnitude and direction that is determined by the individual vectors being added.
When Two vectors have unequal magnitude can their sum be zero explain reason?
No two vectors of unequal magnitude cannot give the sum 0 because for 0 sum the 2 vectors must be equal and in opposite direction
Can the sum of the magnitudes of two vectors ever b equal to the the sum of these two vectors?
Not really. The sum of the magnitudes is a scalar, not a vector - so they can't be equal. But the sum of the two vectors can have the same magnitude, if both vectors point in the same direction.
Is it is possible to add three vectors of equal magnitude and get zero?
Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.
When the angle between two vectors is equal to zero?
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.
Can the resultant of two vectors be equal to zero?
Yes. A vector has magnitude and direction. If the vectors have equal magnitude and directly opposite directions their sum will be zero.
When are magnitudes of two vectors added?
The magnitudes of two vectors are added when the vectors are parallel to each other. In this case, the magnitude of the sum is equal to the sum of the magnitudes of the two vectors.
