Given:
There are three vectors given as
[tex]\begin{gathered} u=(2,3) \\ v=(0,1) \\ w=(4,3) \end{gathered}[/tex]
Required:
We want to find c if u+cw is orthgonal to u
Explanation:
Orthogonal property is dot product of orthogonal vectors is zero
[tex]\begin{gathered} u.(u+cw)=0 \\ (2,3).((2,3)+(4c,3c))=0 \\ (2,3)(2+4c,3+3c)=0 \\ 4+4c+9+9c=0 \\ c=-1 \end{gathered}[/tex]
Final answer:
c = - 1
