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Let hat(i), hat(j) and hat(k ) ?̂ be the...

Let `hat(i), hat(j) and hat(k )` ?̂ be the unit vectors along the three positive coordinate axes. Let `vec(a ) = 3hat(i) +hat(j) -hat(k)` ,
`vec(b) = hat(i) +b_(2)hat(j) +b_(3)hat(k) , " " b_(2)b_(3) in RR`
`vec(c ) = c_(1)hat(i) +c_(2) hat(j) + c_(3) hat(k) , " " c_(1) , c_(2) , c_(3) in RR ` be three vectors such that `b_(2)b_(3) gt 0 vec (a) . vec(b ) = 0 and `
`{:((0,-c_(3),c_(2)),(c_(3),0,-c_(1)),(-c_(2),c_(1),0)):}((1),(b_(2)),(b_(3))) = ((3-c_(1)),(1-c_(2)),(-1-c_(3)))` Then, which of the following is/are TRUE ?

A

`vec(a ).vec(c )=0`

B

`vec(b ).vec(c )=0`

C

`|vec(b)| gt sqrt(10)`

D

`|vec(c )| le sqrt(11)`

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