The number of all possible triplets `(a_(1),a_(2),a_(3))` such that ` a_(1)+a_(2) cos 2x +a_(3) , sin^(2)x=0` for all x is

Options

A. vectors `a=a_1hat(i)+a_2hat(j)+a_3hat(k) and b=4hat(i)+2hat(j)+hat(k)` are perpendicular to each other
B. vectors `a=a_1hat(i)+a_2hat(j)+a_3hat(k) and b=-hat(i)+hat(j)+hat(k)` are perpendicular to each other
C. if vectors `a=a_1hat(i)+a_2hat(j)+a_3hat(k)` is of length `sqrt(6)` units, then one of the ordered triplet `(a_1, a_2, a_3)=(1, -1, -2)`
D. if vectors `2a_1+3a_2+6a_3`, then `|a_1hat(i)+a_2hat(j)+a_3hat(k)|` is `2sqrt(6)`.

Answer

A, B, C, D