(Solved): Find vector \\( \\mathbf{u} \\) with the magnitude given that satisfies the given conditions. \\( \ ...

Find vector \\( \\mathbf{u} \\) with the magnitude given that satisfies the given conditions. \\( \\mathbf{v}=\\langle 3,-1,7\\rangle, \\quad\\|\\mathbf{u}\\|=16, \\quad \\mathbf{u} \\) and \\( \\mathbf{v} \\) have the same direction \\( \\mathbf{u}= \\)\r\n\r\nVectors \\( \\mathbf{a}, \\mathbf{b} \\), and \\( \\mathbf{c} \\) are given. Determine the vectors \\( (\\mathbf{a} \\cdot \\mathbf{b}) \\mathbf{c} \\) and \\( (\\mathbf{a} \\cdot \\mathbf{c}) \\mathbf{b} \\). Express the vectors in component form. \\[ \\mathbf{a}=\\langle 4,0,-2\\rangle, \\mathbf{b}=\\langle-3,-5,1\\rangle, \\mathbf{c}=\\langle 1,1,-1\\rangle \\] \\[ (\\mathbf{a} \\cdot \\mathbf{b}) \\mathbf{c}= \\] \\[ (\\mathbf{a} \\cdot \\mathbf{c}) \\mathbf{b}= \\]