The length of the sum of the vectors `veca = 3hati` and `b = 4hatj` is

Options

A. 3
B. 4
C. 5
D. none of these

Explanation

To find the length of the sum of the vectors \(\vec{a} = 3\hat{i}\) and \(\vec{b} = 4\hat{j}\), we can follow these steps:

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

### Step 2: Sum the vectors
To find the resultant vector \(\vec{V}\), we add \(\vec{a}\) and \(\vec{b}\):
\[ \vec{V} = \vec{a} + \vec{b} = 3\hat{i} + 4\hat{j} \]

### Step 3: Calculate the magnitude of the resultant vector
The magnitude (length) of the vector \(\vec{V}\) can be calculated using the formula:
\[ |\vec{V}| = \sqrt{(V_x)^2 + (V_y)^2} \]
where \(V_x\) and \(V_y\) are the components of the vector \(\vec{V}\).

In our case:
\[ V_x = 3 \quad \text{and} \quad V_y = 4 \]
Thus, the magnitude is:
\[ |\vec{V}| = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \]

### Step 4: Conclusion
The length of the sum of the vectors \(\vec{a}\) and \(\vec{b}\) is:
\[ 5 \]