Question

If $\stackrel{\_}{a},\stackrel{\_}{b,}\stackrel{\_}{c}$ are non-coplanar unit that $\stackrel{\_}{a}\times (\stackrel{\_}{b}\times \stackrel{\_}{c})=\frac{\stackrel{\_}{b}+\stackrel{\_}{c}}{\sqrt{2}}$, then the angle between $\stackrel{\_}{a}$ and $\stackrel{\_}{b}$ is

• A. $\frac{3\pi }{4}$
• B. $\frac{\pi }{4}$
• C. $\frac{\pi }{2}$
• D. none of these

Answer 1

The correct option is A $\frac{3\pi }{4}$

Given,

$a\times (b\times c)=\frac{b+c}{\sqrt{2}}$

$\Rightarrow (a\cdot c)b-(a\cdot b)c$

$\Rightarrow \frac{b+c}{\sqrt{2}}$

$\Rightarrow (a\cdot c-\frac{1}{\sqrt{2}})b-\left(\right(a\cdot b)+\frac{1}{\sqrt{2}})c=0$

$\therefore a\cdot b+\frac{1}{\sqrt{2}}=0$

$\Rightarrow a\cdot b=-\frac{1}{\sqrt{2}}$

$\cos \theta =-\frac{1}{\sqrt{2}}$

$\Rightarrow \theta =\frac{3\pi }{4}$