What is the property of two vectores `vec A and vec B` if:
(A) `|vecA + vecB|= |vecA - vecB|` (b) `vecA + vecB = vecA - vecB`

Explanation

(a) We know that
`" "|vecA +vecB|=sqrt([A^(2) + B^(2) + 2AB cos theta])`
`and " "|vecA -vecB|= sqrt([A^(2) + B^(2) - 2AB cos theta])`
According to gives problem
`sqrt([A^(2) + B^(2) + 2AB cos theta ])= sqrt([A^(2) + B^(2) - 2AB cos theta ])`
Which on solution gives `costheta= 0`, i.e. `theta= pi//2`
i.e., the vectors `vecA` and `vecB` are perppendicular to each other .
(b) Given that `vecA + vecB = vecA -vecB`
`i. e., " "2vecB = 0 or vecB=0`
`i. e., vecB "is a null vector"`.