If `vec(A) = a_(x)hat(i) + a_(y)hat(j) + a_(z)hat(k)` and `vec(B) = b_(x)hat(i) + b_(y)hat(j)+b_(z)hat(k)`. Then the component of `vec(B) + vec(A)` along z-axis is :

Options

A. `b_(z) - a_(z)`
B. `a_(z) - b_(z)`
C. `a_(z) + b_(z)`
D. `(b_(z) - a_(z))/(2)`

Answer

To solve the problem, we need to find the component of the vector sum \(\vec{A} + \vec{B}\) along the z-axis. Let's break this down step by step.

### Step 1: Write the vectors
Given:
\[ \vec{A} = a_x \hat{i} + a_y \hat{j} + a_z \hat{k} \]
\[ \vec{B} = b_x \hat{i} + b_y \hat{j} + b_z \hat{k} \]

### Step 2: Add the vectors
To find \(\vec{A} + \vec{B}\), we add the corresponding components of the vectors:
\[ \vec{A} + \vec{B} = (a_x + b_x) \hat{i} + (a_y + b_y) \hat{j} + (a_z + b_z) \hat{k} \]

### Step 3: Identify the component along the z-axis
The component of the resultant vector \(\vec{A} + \vec{B}\) along the z-axis is the coefficient of \(\hat{k}\) in the vector sum. From our addition in Step 2, the z-component is:
\[ \text{Component along z-axis} = a_z + b_z \]

### Final Answer
Thus, the component of \(\vec{B} + \vec{A}\) along the z-axis is:
\[ a_z + b_z \]

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