Let `vec(a)=hat(i)+2hat(j)` and `vec(b)=2hat(i)+hat(j)`.
(i) Then, `|vec(a)|=|vec(b)|`
(ii) Then vectors `vec(a)` and `vec(b)` are equal.

Answer

To solve the question, we need to analyze the two statements about the vectors \(\vec{a}\) and \(\vec{b}\).

Given:
\[ \vec{a} = \hat{i} + 2\hat{j} \]
\[ \vec{b} = 2\hat{i} + \hat{j} \]

### Step 1: Find the magnitudes of \(\vec{a}\) and \(\vec{b}\)

The magnitude of a vector \(\vec{v} = x\hat{i} + y\hat{j} + z\hat{k}\) is given by the formula:
\[ |\vec{v}| = \sqrt{x^2 + y^2 + z^2} \]

#### For \(\vec{a}\):
\[ |\vec{a}| = \sqrt{(1)^2 + (2)^2} = \sqrt{1 + 4} = \sqrt{5} \]

#### For \(\vec{b}\):
\[ |\vec{b}| = \sqrt{(2)^2 + (1)^2} = \sqrt{4 + 1} = \sqrt{5} \]

### Conclusion for Statement (i):
Since \( |\vec{a}| = \sqrt{5} \) and \( |\vec{b}| = \sqrt{5} \), we can conclude that:
\[ |\vec{a}| = |\vec{b}| \]
Thus, Statement (i) is **TRUE**.

### Step 2: Check if the vectors \(\vec{a}\) and \(\vec{b}\) are equal

Two vectors are equal if their corresponding components are equal.

#### Components of \(\vec{a}\):
- \(x\) component: \(1\)
- \(y\) component: \(2\)

#### Components of \(\vec{b}\):
- \(x\) component: \(2\)
- \(y\) component: \(1\)

Since the \(x\) component of \(\vec{a}\) (which is \(1\)) is not equal to the \(x\) component of \(\vec{b}\) (which is \(2\)), and the \(y\) component of \(\vec{a}\) (which is \(2\)) is not equal to the \(y\) component of \(\vec{b}\) (which is \(1\)), we conclude that:
\[ \vec{a} \neq \vec{b} \]
Thus, Statement (ii) is **FALSE**.

### Final Answer:
(i) TRUE
(ii) FALSE