Скачать или смотреть JEE ADVANCED 2022 VECTOR PYQ | LET i,j and k be unit vector along 3 positive

JEE ADVANCED 2022 | VECTOR | LET i,j and k be unit vector along 3 positive coordinate axes .
let a =3i+j-k , b= i + b2j +b3k , c = c1i +c2j+c3k
Let \( \hat{i}, \hat{j} \) and \( \hat{k} \) be the unit vectors along the three positive coordinate axes. Let
\[
\begin{aligned}
\vec{a} & =3 \hat{i}+\hat{j}-\hat{k} \\
\vec{b} & =\hat{i}+b_{2} \hat{j}+b_{3} \hat{k}, b_{2}, b_{3} \in R \\
\vec{c} & =c_{1} \hat{i}+c_{2} \hat{j}+c_{2} \hat{k}, c_{1}, c_{2}, c_{3} \in R
\end{aligned}
\]
be three vectors such that \( b_{2} b_{3}0, \vec{a} \cdot \vec{b}=0 \) and
\[
\left(\begin{array}{ccc}
0 & -c_{3} & c_{2} \\
c_{3} & 0 & -c_{1} \\
-c_{2} & c_{1} & 0
\end{array}\right)\left(\begin{array}{l}
1 \\
b_{2} \\
b_{3}
\end{array}\right)=\left(\begin{array}{c}
3-c_{1} \\
1-c_{2} \\
-1-c_{3}
\end{array}\right)
\]
Then, which of the following is/are TRUE?
(a) \( \vec{a} \cdot \vec{c}=0 \)
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