Search any question & find its solution
Question:
Answered & Verified by Expert
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:
Solution:
1730 Upvotes
Verified Answer
The correct answer is:
$90^{\circ}$
According to the question:
$\begin{aligned}
|\vec{A}+\vec{B}| & =|\vec{A}-\vec{B}| \\
\Rightarrow |\vec{A}+\vec{B}|^2 & =|\vec{A}-\vec{B}|^2
\end{aligned}$
$\begin{aligned}
& A^2+B^2+2 A B=A^2+B^2-2 A B \\
& 4 \vec{A} \cdot \vec{B}=0 \\
& \vec{A} \cdot \vec{B}=0 \\
& \Rightarrow A B \cos \theta=0 \\
& \Rightarrow \theta=90^{\circ} \\
& {[\text {As } A=B \neqeq 0] }
\end{aligned}$
$\begin{aligned}
|\vec{A}+\vec{B}| & =|\vec{A}-\vec{B}| \\
\Rightarrow |\vec{A}+\vec{B}|^2 & =|\vec{A}-\vec{B}|^2
\end{aligned}$
$\begin{aligned}
& A^2+B^2+2 A B=A^2+B^2-2 A B \\
& 4 \vec{A} \cdot \vec{B}=0 \\
& \vec{A} \cdot \vec{B}=0 \\
& \Rightarrow A B \cos \theta=0 \\
& \Rightarrow \theta=90^{\circ} \\
& {[\text {As } A=B \neqeq 0] }
\end{aligned}$
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.