Vector Algebra

If \(\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) and \(\mathbf{c}=x \hat{\mathbf{i}}+(x-2) \hat{\mathbf{j}}-\hat{\mathbf{k}}\) and if the vector \(\mathbf{c}\) lies in the plane of vectors \(\mathbf{a}\) and \(\mathbf{b}\) and then \(x\) equals