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the sum of two vectors cannot be equal to the the difference of the two vectors

Is it possible that the magnitude of the sum and difference of two vextors be equal to each other?

Nishchal asked the Naked Scientists: Is it possible that the magnitude of the sum and difference of two vextors be equal to each other?What do you think?

LightarrowThat's much neater than my algebraic solution [(a_{x}+b_{x})^{2})+(a_{y}+b_{y})^{2})] - [(a_{x}-b_{x})^{2})+(a_{y}-b_{y})^{2})]=0

Which also ends up with the dot product (a_{x}b_{x} + a_{y}b_{y}) equals zero.Perhaps to fully explain - the dot product of two vectors a.b = |a|.|b|CosΘ where |a| is the magnitude and Θ is the angle between the two vectors. For the dot product |a|.|b|CosΘ to equal zero either magnitude of a or b must be zero or CosΘ must be zero - and that happens when Θ is 90 or 270 degrees.