Let \(\vec{\text{a}}=2{\hat{i}}−3{\hat {j}}+4{\hat {k}},\vec{\text{b}}=7\vec{\text{i}}+2\vec{\text{j}}−3\vec{\text{k}},\vec{\text{c}}=\vec{\text{i}}+\vec{\text{j}}+\vec{\text{k}}\). The vector \(\vec{\text{x}}\) such that \(\vec{\text{x}}\cdot\vec{\text{c}}\) = 60 and perpendicular to both \(\vec{\text{a}},\vec{\text{b}}\) is:
1
\(14\vec{\text{i}}−6\vec{\text{j}}−12\vec{\text{k}}\)
2
\(\vec{\text{i}}+34\vec{\text{j}}+25\vec{\text{k}}\)
3
\(4\vec{\text{i}}−21\vec{\text{j}}−12\vec{\text{k}}\)
4
\(6\vec{\text{i}}−6\vec{\text{j}}+28\vec{\text{k}}\)