If `vec(a)=2hat(i)+2hat(j)+3hat(k)`, then its magnitude is :

Options

A. 17
B. `sqrt(17)`
C. 34
D. None of these

Answer

To find the magnitude of the vector \(\vec{A} = 2\hat{i} + 2\hat{j} + 3\hat{k}\), we will follow these steps:

### Step 1: Identify the components of the vector
The vector \(\vec{A}\) has the following components:
- \(x = 2\) (coefficient of \(\hat{i}\))
- \(y = 2\) (coefficient of \(\hat{j}\))
- \(z = 3\) (coefficient of \(\hat{k}\))

### Step 2: Use the formula for the magnitude of a vector
The magnitude of a vector \(\vec{A} = x\hat{i} + y\hat{j} + z\hat{k}\) is given by the formula:
\[ |\vec{A}| = \sqrt{x^2 + y^2 + z^2} \]

### Step 3: Substitute the values into the formula
Now, substituting the values of \(x\), \(y\), and \(z\) into the formula:
\[ |\vec{A}| = \sqrt{2^2 + 2^2 + 3^2} \]

### Step 4: Calculate the squares of the components
Calculating the squares:
- \(2^2 = 4\)
- \(2^2 = 4\)
- \(3^2 = 9\)

### Step 5: Add the squares
Now, add these values together:
\[ |\vec{A}| = \sqrt{4 + 4 + 9} = \sqrt{17} \]

### Step 6: Write the final answer
Thus, the magnitude of the vector \(\vec{A}\) is:
\[ |\vec{A}| = \sqrt{17} \]