Consider two vectors `vecF_(1)=2hati+5hatk` and `vecF_(2)=3hatj+4hatk`. The magnitude to thhe scalar product of these vectors is

Options

A. 20
B. 23
C. `5sqrt(33)`
D. 26

Answer

To find the magnitude of the scalar product (dot product) of the vectors \(\vec{F_1} = 2\hat{i} + 5\hat{k}\) and \(\vec{F_2} = 3\hat{j} + 4\hat{k}\), we can follow these steps:

### Step 1: Write down the vectors
We have:
\[ \vec{F_1} = 2\hat{i} + 5\hat{k} \]
\[ \vec{F_2} = 3\hat{j} + 4\hat{k} \]

### Step 2: Calculate the dot product
The dot product of two vectors \(\vec{A} = a_1\hat{i} + b_1\hat{j} + c_1\hat{k}\) and \(\vec{B} = a_2\hat{i} + b_2\hat{j} + c_2\hat{k}\) is given by:
\[ \vec{A} \cdot \vec{B} = a_1a_2 + b_1b_2 + c_1c_2 \]

For our vectors:
- \(\vec{F_1} = 2\hat{i} + 0\hat{j} + 5\hat{k}\) (where \(b_1 = 0\))
- \(\vec{F_2} = 0\hat{i} + 3\hat{j} + 4\hat{k}\) (where \(a_2 = 0\))

Now, substituting the components into the dot product formula:
\[ \vec{F_1} \cdot \vec{F_2} = (2)(0) + (0)(3) + (5)(4) \]
\[ = 0 + 0 + 20 = 20 \]

### Step 3: Find the magnitude of the scalar product
The magnitude of the scalar product is simply the absolute value of the result we obtained:
\[ |\vec{F_1} \cdot \vec{F_2}| = |20| = 20 \]

### Final Answer
The magnitude of the scalar product of the vectors \(\vec{F_1}\) and \(\vec{F_2}\) is:
\[ \boxed{20} \]