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

Options

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

Explanation

To solve the problem, we need to find the mass of the body given the force vector and the acceleration. We will use Newton's second law of motion, which states that:

\[ \vec{F} = m \cdot \vec{a} \]

Where:
- \( \vec{F} \) is the force vector,
- \( m \) is the mass,
- \( \vec{a} \) is the acceleration vector.

### Step-by-Step Solution:

1. **Identify the Force Vector**:
The force vector is given as:
\[ \vec{F} = 6\hat{i} - 8\hat{j} + 10\hat{k} \]

2. **Calculate the Magnitude of the Force**:
The magnitude of the force vector \( \vec{F} \) can be calculated using the formula:
\[ |\vec{F}| = \sqrt{(F_x)^2 + (F_y)^2 + (F_z)^2} \]
Where \( F_x = 6 \), \( F_y = -8 \), and \( F_z = 10 \).

Substituting the values:
\[ |\vec{F}| = \sqrt{(6)^2 + (-8)^2 + (10)^2} = \sqrt{36 + 64 + 100} = \sqrt{200} \]
Simplifying further:
\[ |\vec{F}| = 10\sqrt{2} \]

3. **Identify the Acceleration**:
The acceleration is given as:
\[ \vec{a} = 1 \, \text{m/s}^2 \]

4. **Use Newton's Second Law to Find Mass**:
According to Newton's second law:
\[ \vec{F} = m \cdot \vec{a} \]
Rearranging for mass \( m \):
\[ m = \frac{|\vec{F}|}{|\vec{a}|} \]
Substituting the values:
\[ m = \frac{10\sqrt{2}}{1} = 10\sqrt{2} \, \text{kg} \]

5. **Final Answer**:
Therefore, the mass of the body is:
\[ m = 10\sqrt{2} \, \text{kg} \]