Question

if vector vector A are such that |vector A+vector B|=|vector A|=|vector B|then|vector A-vectorB| may be equated to​

Answer 1

Answer:

vector a - vector b = a√3

Explanation:

vector a + vector b = vector a = vector b

⇒   vector a = vector b

vector a + vector b = √a² +b² +2ab.cosФ

from the given we know that,

vector a + vector b = vector a

⇒ vector a = √a² +b² +2ab.cosФ

on squaring both the sides,

a² = a² + b² + 2ab.cosФ

and we know from above vector a = vector b

⇒ a²= a² + a² +2aa.cosФ

a² = 2a² + 2a².cosФ

a² = 2a²( 1 + cosФ )

1÷2 = 1 + cosФ

cosФ = -1÷2

we know that it is possible only when Ф = 120 degree

now a-b = √a² +b² - 2ab.cos(120)

= √2a²- 2a²× -1÷2

= √2a²+a²

=√3a²

= a√3

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