0
Can the magnitude of the sum of two two vectors be equal to the magnitude of difference of two vectors?
Wiki User
∙ 12y ago
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)|.
Wiki User
∙ 12y ago
Add your answer:
Earn +20 pts
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?
iff the angle between them is 120 degrees
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 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.
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.
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 sum of two vectors be equal to either of vectors Explain?
Only if one of them has a magnitude of zero, so, effectively, no.
When is the vector sum of two quatities equal in magnitude to the scalar sum?
When all the vectors have the same direction.
