Question

Let a = a₁i +a₂j + a₃k, b = b₁i + b₂j + b₃k and c = c₁i + c₂j + c₃k be three non-zero vectors such that c is a unit vector perpendicular to both a and b. If the angle between a and b is \(\cfrac{\pi}6,\) then \(\begin{vmatrix} a_1 & a_2& a_3\\ b_1& b_2& b_3\\ c_1& c_2& c_3 \end{vmatrix}^2\)is equal to 

A. 0

B. 1

C. \((\cfrac14)|\vec a|^2|\vec b|^2\)

D. \((\cfrac34)|\vec a|^2|\vec b|^2\)

Answer 1

Correct option is C. \((\cfrac14)|\vec a|^2|\vec b|^2\) 

(∵ \(\vec c\) is perpendicular to \(\vec a\) and \(\vec b\) ⇒ angle is 0)