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, $b \times (c \times a) = \frac{c}{2}$
$ ⇒ ( b . a) c - ( b .c) a = \frac{c}{2}$
$ ⇒ b . a = \frac{1}{2}$ and $ b .c = 0$
$∴$ Angle between $ b$ and $c = 90^{\circ}$ and angle between $b$ and $a$ is $60^{\circ}$.