Angle between two vector

1.	Angle between two vector
Answer» Given : \|a + B\| = \|a - b\| To find : The angle between a and b Solution : we know that, » If two vectors of magnitudes are acting at an angle, then the MAGNITUDE of their RESULTANT is given by PARALLELOGRAM law that is, $\sf \|a + b\| = \sqrt{ {a}^{2} + {b}^{2} + 2abcos \theta }$ SIMILARLY, $\sf \|a - b\| = \sqrt{ {a}^{2} + {b}^{2} - 2abcos \theta }$ According to Question, $\dashrightarrow\sf \|a + b\| = \|a - b\|$ $\dashrightarrow\sf \sqrt{ {a}^{2} + {b}^{2} + 2abcos \theta } = \sqrt{ {a}^{2} + {b}^{2} - 2abcos \theta } \\$ $\dashrightarrow\sf {a}^{2} + {b}^{2} + 2abcos \theta = {a}^{2} + {b}^{2} - 2abcos \theta \\$ $\dashrightarrow\sf \not{a}^{2} + \not {b}^{2} + 2abcos \theta - \not{a}^{2} - \not{b}^{2} + 2abcos \theta = 0 \\$ $\dashrightarrow\sf 2ab \: cos \theta + 2ab \: cos \theta = 0$ $\dashrightarrow\sf 4ab \: cos \theta = 0$ $\dashrightarrow\sf cos \theta = 0$ $\dashrightarrow\sf cos \theta = cos \: 90 \degree$ $\dashrightarrow\sf \theta = 90 \degree$ Thus, Angle between two vectors is 90°

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