Answer:
[tex]90^\circ[/tex]
Step-by-step explanation:
Given two non zero vectors, [tex]\vec a, \vec b[/tex].
Let the angle between the two vectors = [tex]\theta[/tex]
Given that:
[tex]|\vec a+\vec b|=|\vec a-\vec b|[/tex]
Let us have a look at the formula for magnitude of addition of two vectors:
[tex]|\vec x+\vec y|=\sqrt{x^2+y^2+2xycos\theta}[/tex]
Where [tex]\theta[/tex] is the angle between the two vectors.
formula for magnitude of subtraction of two vectors:
[tex]|\vec x-\vec y|=\sqrt{x^2+y^2-2xycos\theta}[/tex]
As per the given condition:
[tex]\sqrt{a^2+b^2+2abcos\theta}=\sqrt{a^2+b^2-2abcos\theta}[/tex]
Squaring both sides:
[tex]a^2+b^2+2abcos\theta=a^2+b^2-2abcos\theta\\\Rightarrow 2abcos\theta=-2abcos\theta\\\Rightarrow cos\theta = -cos\theta\\\Rightarrow 2cos\theta = 0\\\Rightarrow cos\theta = 0\\\Rightarrow \theta = 90^\circ[/tex]
So, the angle between the two vectors is: [tex]90^\circ[/tex]
