`a_1, a_2, a_3, in R-{0}` and `a_1+a_2cos2x+a_3sin^2x=0fora l lx in R ,` then vector ` vec a=a_1 hat i+a_2 hat j+a_3 hat ka n d vec b=4 hat i+2 hat j+ hat k` are perpendicular to each other vector ` vec a=a_1 hat i+a_2 hat j+a_3 hat ka n d vec b=- hat i+ hat j+2 hat k` are parallel to each other vector ` vec a=a_1 hat i+a_2 hat j+a_3 hat k` is of length`sqrt(6)` units, then one of the ordered triple `(a_1, a_2, a_3)=(1,-1,-2)` are perpendicular to each other if `2a_1+3a_2+6a_3=26 ,t h e n|a_1 hat i+a_2 hat j+a_3 hat k|i s2sqrt(6)`

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