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Two vectors A and B have precisely equal magnitudes. In order for the magnitude of A + B to be larger than the magnitude of A - B by the factor n, what must be the angle between them?​

Respuesta :

evgeniylevi

Answer:

[tex]\alpha=arccos[\frac{(a^2+b^2)(n-1)}{2ab(n+1)}].[/tex]

Explanation:

1) for A+B: a²+b²-2abcos(π-α);

2) for A-B: a²+b²-2abcos(α);

3) according to the condition (A+B):(A-B)=n, then

[tex]n=\frac{a^2+b^2-2abcos(\pi-a)}{a^2+b^2-2abcos(a)}; \ = > \ n=\frac{a^2+b^2+2abcos(a)}{a^2+b^2-2abcos(a)}; \ = > \ cos(\alpha)=\frac{(a^2+b^2)(n-1)}{2ab(n-1)}.[/tex]

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