Question

If $|\vec {a} |=7$ and $|\vec {b} |=11,$ then the angle between the vectors $\vec {a} +\vec {b}$ and $\vec {a} -\vec {b}$ is equal to

• A. $\pi$
• B. $\frac{5\pi }{6}$
• C. $\frac{2\pi }{3}$
• D. $\frac{3\pi }{4}$

Answer 1

Answer: (A)

$\pi$

Answer 2

Given, $|a|=7$ and $|b|=11$
The angle between vectors $a+b$ and $a-b$ is $\cos \theta =\frac{(a+b)\,.\,(a-b)}{|a+b|\,.\,|a-b|}=\frac{|a{{|}^{2}}-|b{{|}^{2}}}{18.4}$ $|\because |a+b|\le |a|+|b||a-b|\ge |a|-|b|$
$=\frac{49-121}{18.4}=\frac{-72}{72}=-1$
$\Rightarrow$ $\cos \,\theta =cos\,\pi$
$\Rightarrow$ $\theta =\pi$