Question

If (A vector + B vector) . (A vector - B vector )= 0, then show that the magnitude of both the vectors are equal.

plz help anyone...... plzzzzz

Answer 1

Hey

|a+b|=|a−b

|a+b|2=|a−b|2

We know for any vector v, v⋅v=|v|2

(a+b)⋅(a+b)=(a−b)⋅(a−b)

a⋅a+a⋅b+b⋅a+b⋅b=a⋅a−a⋅b−b⋅a+b⋅b

2(a⋅b)=−2(a⋅b)

4(a⋅b)=0

a⋅b=0

We know that the dot product of two vectors a and b can be found using a⋅b=|a||b|cosθ (θθ is the acute angle between the two vectors)

|a||b|cosθ=0

Since |a||a| and |b||b| are probably not 0 (the vectors have a length),

cosθ=0

∴θ=arccos0

θ=π2=90o

Therefore the (acute) angle between them is π2, or 90o ie they are orthogonal.


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