If vector(a) = i + j + k and vector(b) = j - k then find a vector vector(c)

Question

If \(\vec{a}=\hat{i}+\hat{j}+\hat{k}\) and \(\vec{b}=\hat{j}-\hat{k}\) then find a vector \(\vec{c}\) such that \(\vec{a}\times \vec{c}=\vec{b}\) and \(\vec{a}\,. \vec{c}=3.\)

Answer 1

On solving \(c_1 - c_2 = 1\) and \(2c_1 - c_2 = 4\) we get