Given `vec(A)=0.3hati+0.4hatj+chatk` calculate the value of c if A is a unit vector.

Explanation

To solve the problem, we need to find the value of \( c \) in the vector \( \vec{A} = 0.3 \hat{i} + 0.4 \hat{j} + c \hat{k} \) given that \( \vec{A} \) is a unit vector. A unit vector has a magnitude of 1.

### Step-by-Step Solution:

1. **Understanding the Magnitude of a Vector**:
The magnitude of a vector \( \vec{A} = a \hat{i} + b \hat{j} + c \hat{k} \) is given by the formula:
\[
|\vec{A}| = \sqrt{a^2 + b^2 + c^2}
...