Question

If a and b are vectors such that $|a+b|=|a-b|$ then the angle between a and b is

• A. 60$^\circ$
• B. 120$^\circ$
• C. 30$^\circ$
• D. 90$^\circ$

Answer 1

The Correct Option is D

We have, $| a +b | = | a - b |$
On squaring both sides, we get
$|a+b|^2=|a-b|^2$
$\Rightarrow \,|\vec{a} |^2 + |\vec{b}|^2 + 2 \vec{a} . \vec{b} = |\vec{a}|^2 + |\vec{b}|^2 - 2 \vec{a} . \vec{b}$
$\Rightarrow \, 4 \vec{a} .\vec{b} = 0 $
$\Rightarrow \,\vec{a} . \vec{b} = 0 $
$\Rightarrow \, \vec{a}$ and $\vec{b} $ are perpendicular to each other.
So, angle between them is $90^{\circ}$.
Alternative
$\because \, | a + b | = | a - b|$
$ \therefore $ a and b are perpendicular to each other.
So, angle between $a$ and b is $90^{\circ} $