Problem
Let i, j, and k be the unit vectors along the three positive coordinate axes. Let
| a = 3i + j – k, | |
| b = i + b2j + b3k, | b2, b3 ∈ R |
| c = c1i + c2j + c3k, | c1, c2, c3 ∈ R |
be three vectors such that b2b3 > 0, a.b = 0 and
\( \begin{pmatrix}0 & -c_3 & c_2 \\ c_3 & 0 & -c_1 \\ -c_2 & c_1 & 0 \\ \end{pmatrix}\begin{pmatrix}1 \\ b_2\\ b_3\end{pmatrix}= \begin{pmatrix} 3-c_1\\ 1-c_2 \\ -1-c_3 \end{pmatrix} \)
Then, which of the following is / are true?
A a.c = 0
B b.c = 0
C |b| > √10
D |c| ≤ √11