Question

Let $a,b,c$ be three unit vectors such that $b\times (c\times a)=\frac{c}{2}$ .If $a$ and $c$ are non-parallel, then the angles which $b$ makes with $c$ and $a$ are respectively

• A. $30^{\circ }$ & $60^{\circ }$
• B. $60^{\circ }$ & $45^{\circ }$
• C. $30^{\circ }$ & $90^{\circ }$
• D. $90^{\circ }$ & $60^{\circ }$

Answer 1

Answer: (D)

We have, $b\times (c\times a)=\frac{c}{2}$
and $|a|=|b|=|c|=1$
Now, $b\times (c\times a)=\frac{c}{2}$
$\Rightarrow (b.a)c-(b.c)a=\frac{c}{2}$
$\Rightarrow b.a=\frac{1}{2}$ and $b.c=0$
$\therefore$ Angle between $b$ and $c=90^{\circ }$ and angle between $b$ and $a$ is $60^{\circ }$.