Discussion
If the vectors \(\vec{A} = a_{x}\hat{i} + a_{y}\hat{j} + a_{z}\hat{k}\), \(\vec{B} = b_{x}\hat{i} + b_{y}\hat{j} + b_{z}\hat{k}\) and \(\vec{C} = c_{x}\hat{i} + c_{y}\hat{j} + c_{z}\hat{k}\) are defining the vector \(\vec{T} = \vec{A} - \vec{B} + \vec{C}\) , then the \(z\)-component of the vector \(T_{z}\) is
Answer: B
\(T_z\) is \(a_z - b_z + c_z\).
Vectors add and subtract component by component. The z-component of \(\vec{A} - \vec{B} + \vec{C}\) uses only the z-components of the three vectors.
Every other option mixes components from different axes (\(a_x\), \(a_y\) or \(c_x\) with z-components), or gives the y-component \(a_y - b_y + c_y\) instead. The same rule gives \(T_x = a_x - b_x + c_x\) and \(T_y = a_y - b_y + c_y\).
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