Question

If the angle between vectors a- bis an acute angle, then the difference a - bis :​

Answer 1

Answer:

We can visualize the sum and difference of vectors as diagonals of a parallelogram. In the diagram above, c⃗ =b⃗ +a⃗ and d⃗ =b⃗ −a⃗ . The equation |b⃗ +a⃗ |=|b⃗ −a⃗ | implies that the diagonals of the parallelogram are equal. This implies that the triangles △ABD and △ACD are congruent, since they have three pairs of equal sides. Hence ∠A=∠D . But the sum of those two angles must be 180∘ , since ABCD is a parallelogram. Therefore ∠A=∠D=90∘ .

Explanation:

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