The vectors A and B are such that | A + B |=| A - B | . The angle between the two vectors is:

Correct answer: B. 90^ According to the question: aligned | A + B | & =| A - B | | A + B |^2 & =| A - B |^2 aligned aligned & A^2+B^2+2 A B=A^2+B^2-2 A B & 4 A · B =0 & A · B =0 & A B θ=0 & θ=90^ & [As A=B 0] aligned

NEET 2006

Exam: NEET
Year: 2006
Subject: Physics
Chapter: Mathematics in Physics

NEET 2006 · Physics · Mathematics in Physics

The vectors A and B are such that | A + B |=| A - B | . The angle...

The vectors

\vec{A}

and

\vec{B}

are such that

|\vec{A}+\vec{B}|=|\vec{A}-\vec{B}|

. The angle between the two vectors is:

Options

A $45^{\circ}$
B $90^{\circ}$
C $60^{\circ}$
D $75^{\circ}$

Correct answer

B. $90^{\circ}$

Step-by-step solution

According to the question:

\begin{aligned} |\vec{A}+\vec{B}| & =|\vec{A}-\vec{B}| \\ \Rightarrow |\vec{A}+\vec{B}|^2 & =|\vec{A}-\vec{B}|^2 \end{aligned}

\begin{aligned} & A^2+B^2+2 A B=A^2+B^2-2 A B \\ & 4 \vec{A} \cdot \vec{B}=0 \\ & \vec{A} \cdot \vec{B}=0 \\ & \Rightarrow A B \cos \theta=0 \\ & \Rightarrow \theta=90^{\circ} \\ & {[\text{As } A=B \neqeq 0] } \end{aligned}

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