Can the magnitude if the difference between two vectors ever be greater than the magnitude of their sum?

Answer 1

yes,if the components are making angle 0<=theta<=90

no ,the magnitude of vector can never attain a negative value |a|=square root of both components which always gives a positive value

Answer 2

No. That's the maximum possible resultant. And that only happens when the two vectors

have the same identical direction; otherwise, the magintude of the resultant is less than

the sum of their individual magnitudes.

Answer 3

Yes. For example, if one vector has a length of 1 and points north, and the second vector has a length of 1 and points south, the difference (vector1 minus vector2) will have a length of 2 and point north.

Answer 4

No,even if the y component is zero then the vector will be equall to the x-component,

Answer 5

yes, the magnitude of difference between two mutually perpendicular vectors is greater than magnitude of either vector..

Answer 6

Yes, for example in complex numbers z = 1 -i, i is the "x-component" and here it is negative.

Answer 7

Sure; for example, in one dimension, a vector (+10) and a vector (-10) would have a sum of 0, and a difference of magnitude 10 - (-10) = 20.

Answer 8

Yes; for example if two vectors of magnitude 1 each are in opposite directions their sum is 0 but their difference is 2

Answer 9

No

Answer 10

No.