Let \(x\hat{i}+y\hat{j}+z\hat{k}\) be the unit vector along \(\vec{c}.\) Since \(-\hat{i}+\hat{j}-\hat{k}\) bisects the angle between \(\vec{c}\) and \(3\hat{i}+4\hat{j}.\)
Therefore,
But \(\lambda \neq 0,\) because \(\lambda = 0\) implies that the given vectors are parallel.