Search any question & find its solution
Question:
Answered & Verified by Expert
If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors such that $\mathbf{a}=\mathbf{b}+\mathbf{c}$ and the angle between $\mathbf{b}$ and $\mathbf{c}$ is $\pi / 2$, then
Options:
Solution:
2058 Upvotes
Verified Answer
The correct answer is:
$a^2=b^2+c^2$
Given that $\mathbf{a}=\mathbf{b}+\mathbf{c}$ and angle between $\mathbf{b}$ and $\mathbf{c}$ is $\frac{\pi}{2}$.
So,
$\begin{aligned}
& \mathbf{a}^2=\mathbf{b}^2+\mathbf{c}^2+2 \mathbf{b} \cdot \mathbf{c} \\or \\
& \mathbf{a}^2=\mathbf{b}^2+\mathbf{c}^2+2|\mathbf{b} \| \mathbf{c}| \cos \frac{\pi}{2}
\end{aligned}$
or $\quad \mathbf{a}^2=\mathbf{b}^2+\mathbf{c}^2+0, \quad \therefore \mathbf{a}^2=\mathbf{b}^2+\mathbf{c}^2$
i.e., $a^2=b^2+c^2$.
So,
$\begin{aligned}
& \mathbf{a}^2=\mathbf{b}^2+\mathbf{c}^2+2 \mathbf{b} \cdot \mathbf{c} \\or \\
& \mathbf{a}^2=\mathbf{b}^2+\mathbf{c}^2+2|\mathbf{b} \| \mathbf{c}| \cos \frac{\pi}{2}
\end{aligned}$
or $\quad \mathbf{a}^2=\mathbf{b}^2+\mathbf{c}^2+0, \quad \therefore \mathbf{a}^2=\mathbf{b}^2+\mathbf{c}^2$
i.e., $a^2=b^2+c^2$.
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.