In a Cartesian reference system two vectors are defined as (mathbf{a}=2 c hat{mathbf{i}}-hat{mathbf{j}}+4 hat{mathbf{k}}) and (mathbf{b}=4 hat{mathbf{i}}+)

Question:

In a Cartesian reference system two vectors are defined as $\mathbf{a}=2 c \hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ and $\mathbf{b}=4 \hat{\mathbf{i}}+$ $(c-1) \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$. For which values of $c$ are the two vectors orthogonal?

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