Question

Let $\overline{V}=2i+j-k,\overline{W}=i+3k$, if $\overline{U}$ is a unit vector then the maximum value of $\overline{U}.(\overline{V}\times \overline{W})$ is

• A. $\sqrt{3}$
• B. 7
• C. $\sqrt{59}$
• D. not defined

Answer 1

The correct option is C $\sqrt{59}$

$\overline{U}.(\overline{V}\times \overline{W})=\overline{U}.(3i-7j-k)=|\overline{U}||3i-7j-k|cos\theta =\sqrt{59}cos\theta$
$\therefore$ Maximum value of $[\overline{U},\overline{V},\overline{W}]=\sqrt{59}.(\because cos\theta \le 1)$