A force vector applied on a mass is represented as `F = 6i - 8j + 10k` and acceleration with 1 `m//s^(2)`. What will be the mass of the body ?

Options

A. `10sqrt(2)` kg
B. `2sqrt(10)` kg
C. 10 kg
D. 20 kg

Explanation

To find the mass of the body given the force vector and acceleration, we can follow these steps:

### Step 1: Identify the given values
- The force vector \( F \) is given as:
\[ F = 6\hat{i} - 8\hat{j} + 10\hat{k} \]
- The acceleration \( a \) is given as:
\[ a = 1 \, \text{m/s}^2 \]

### Step 2: Calculate the magnitude of the force vector
To find the magnitude of the force vector \( F \), we use the formula for the magnitude of a vector:
\[ |F| = \sqrt{(F_x)^2 + (F_y)^2 + (F_z)^2} \]
Substituting the components of \( F \):
\[ |F| = \sqrt{(6)^2 + (-8)^2 + (10)^2} \]
Calculating each term:
\[ |F| = \sqrt{36 + 64 + 100} \]
\[ |F| = \sqrt{200} \]
\[ |F| = 10\sqrt{2} \, \text{N} \]

### Step 3: Apply Newton's Second Law
According to Newton's second law, the relationship between force, mass, and acceleration is given by:
\[ F = m \cdot a \]
Where:
- \( F \) is the force,
- \( m \) is the mass,
- \( a \) is the acceleration.

### Step 4: Solve for mass
Rearranging the formula to find mass:
\[ m = \frac{F}{a} \]
Substituting the values we have:
\[ m = \frac{10\sqrt{2}}{1} \]
\[ m = 10\sqrt{2} \, \text{kg} \]

### Conclusion
The mass of the body is:
\[ m = 10\sqrt{2} \, \text{kg} \]

### Final Answer
Thus, the correct option is:
**Option 1: \( 10\sqrt{2} \, \text{kg} \)**

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