Question

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

• A. $a_{x}-b_{x}+c_{z}$
• B. $a_{z}-b_{z}+c_{z}$
• C. $a_{y}-b_{z}+c_{z}$
• D. $a_{z}-b_{z}+c_{x}$
• E. $a_{y}-b_{y}+c_{y}$

Hint:

Logic Tip: In linear vector operations, independent axes never mix. You don't need to write out the full equation. The operation is $\vec{A}-\vec{B}+\vec{C}$. For the z-component, simply grab the z-terms and apply the same signs: $a_z - b_z + c_z$.

Answer 1

The Correct Option is B