Search any question & find its solution
Question:
Answered & Verified by Expert
If $a$ and $b$ are vectors such that $|a \times b|=|a-b|$, then the angle between a and b is
Options:
Solution:
2154 Upvotes
Verified Answer
The correct answer is:
$90^{\circ}$
We have,
$$
\begin{aligned}
& &|a+b| &=|a-b| \\
& \Rightarrow &|a+b|^{2} &=|a-b|^{2} \\
\Rightarrow & &(a+b) \cdot(a+b) &=\langle a-b) \cdot(a-b) \\
& \Rightarrow &|a|^{2}+|b|^{2}+2 a \cdot b &=|a|^{2}+|b|^{2}-2 a \cdot b \\
\Rightarrow & & 4 a \cdot b &=0 \\
& \Rightarrow & a \cdot b &=0 \\
& \Rightarrow & a & \perp b
\end{aligned}
$$
So, angle between a and $\mathrm{b}$ is $90^{\circ}$.
$$
\begin{aligned}
& &|a+b| &=|a-b| \\
& \Rightarrow &|a+b|^{2} &=|a-b|^{2} \\
\Rightarrow & &(a+b) \cdot(a+b) &=\langle a-b) \cdot(a-b) \\
& \Rightarrow &|a|^{2}+|b|^{2}+2 a \cdot b &=|a|^{2}+|b|^{2}-2 a \cdot b \\
\Rightarrow & & 4 a \cdot b &=0 \\
& \Rightarrow & a \cdot b &=0 \\
& \Rightarrow & a & \perp b
\end{aligned}
$$
So, angle between a and $\mathrm{b}$ is $90^{\circ}$.
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.