If `vecA = 3hati - 4hatj` and `vecB = -hati - 4hatj`, calculate the direction of `vecA- vecB`.

Options

A. along positive x-axis
B. along negative x-axis
C. along positive y-axis
D. along negative y-axis

Answer

To solve the problem of finding the direction of the vector \(\vec{A} - \vec{B}\), we will follow these steps:

### Step 1: Write down the vectors
We have:
\[ \vec{A} = 3\hat{i} - 4\hat{j} \]
\[ \vec{B} = -\hat{i} - 4\hat{j} \]

### Step 2: Calculate \(\vec{A} - \vec{B}\)
To find \(\vec{A} - \vec{B}\), we subtract the components of \(\vec{B}\) from those of \(\vec{A}\):
\[ \vec{A} - \vec{B} = (3\hat{i} - 4\hat{j}) - (-\hat{i} - 4\hat{j}) \]
This simplifies to:
\[ \vec{A} - \vec{B} = 3\hat{i} - 4\hat{j} + \hat{i} + 4\hat{j} \]
Combining like terms gives:
\[ \vec{A} - \vec{B} = (3 + 1)\hat{i} + (-4 + 4)\hat{j} = 4\hat{i} + 0\hat{j} \]
Thus, we have:
\[ \vec{A} - \vec{B} = 4\hat{i} \]

### Step 3: Determine the direction of \(\vec{A} - \vec{B}\)
The vector \(4\hat{i}\) indicates that the resultant vector is directed along the positive x-axis.

### Step 4: Express the direction in terms of angles
The direction of a vector can also be expressed in terms of an angle \(\theta\) with respect to the positive x-axis. Since the vector has no y-component, the angle is:
\[ \theta = 0^\circ \]

### Final Answer
The direction of \(\vec{A} - \vec{B}\) is along the positive x-axis, which corresponds to an angle of \(0^\circ\).

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