Search any question & find its solution
Question:
Answered & Verified by Expert
If $a$ and $b$ are unit vectors and $\mid$ a $+b \mid=1$, then $\mid$ a $-b \mid$ is equal to
Options:
Solution:
1821 Upvotes
Verified Answer
The correct answer is:
$\sqrt{3}$
We have
$$
|a|=|b|=1,|a+b|=1
$$
We know that,
$$
\begin{aligned}
& \Rightarrow &|\mathbf{a}+\mathbf{b}|^{2}+|\mathbf{a}-\mathbf{b}|^{2} &=2\left(|\mathbf{a}|^{2}+|\mathbf{b}|^{2}\right) \\
\Rightarrow \quad(1)^{2}+|\mathbf{a}-\mathbf{b}|^{2} &=2\left((1)^{2}+(1)^{2}\right) \\
1+|\mathbf{a}-\mathbf{b}|^{2} &=4 \\
\Rightarrow \quad & &|\mathbf{a}-\mathbf{b}| &=\sqrt{3}
\end{aligned}
$$
$$
|a|=|b|=1,|a+b|=1
$$
We know that,
$$
\begin{aligned}
& \Rightarrow &|\mathbf{a}+\mathbf{b}|^{2}+|\mathbf{a}-\mathbf{b}|^{2} &=2\left(|\mathbf{a}|^{2}+|\mathbf{b}|^{2}\right) \\
\Rightarrow \quad(1)^{2}+|\mathbf{a}-\mathbf{b}|^{2} &=2\left((1)^{2}+(1)^{2}\right) \\
1+|\mathbf{a}-\mathbf{b}|^{2} &=4 \\
\Rightarrow \quad & &|\mathbf{a}-\mathbf{b}| &=\sqrt{3}
\end{aligned}
$$
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.