Let `a=12hati+nhatj and |a|=13`, find th value of n.

Explanation

To solve the problem, we need to find the value of \( n \) given the vector \( \mathbf{a} = 12 \hat{i} + n \hat{j} \) and its magnitude \( |\mathbf{a}| = 13 \).

### Step-by-Step Solution:

1. **Write the expression for the magnitude of the vector**:
The magnitude of a vector \( \mathbf{a} = x \hat{i} + y \hat{j} \) is given by the formula:
\[
|\mathbf{a}| = \sqrt{x^2 + y^2}
...