The vectors are given below
` veca = hati + 2hatj +3hatk vecb = 2hati + 4hatj + 6hatk and vecc = 3hati + 6hatj + 9 hatk`
find the components of the vector ` veca + vecb -vecc`

Answer

To solve the problem of finding the components of the vector \( \vec{a} + \vec{b} - \vec{c} \), we will follow these steps:

### Step 1: Write down the vectors
The vectors are given as:
- \( \vec{a} = \hat{i} + 2\hat{j} + 3\hat{k} \)
- \( \vec{b} = 2\hat{i} + 4\hat{j} + 6\hat{k} \)
- \( \vec{c} = 3\hat{i} + 6\hat{j} + 9\hat{k} \)

### Step 2: Add the vectors \( \vec{a} \) and \( \vec{b} \)
To find \( \vec{a} + \vec{b} \), we add the corresponding components of \( \vec{a} \) and \( \vec{b} \):
- \( \text{x-component: } 1 + 2 = 3 \)
- \( \text{y-component: } 2 + 4 = 6 \)
- \( \text{z-component: } 3 + 6 = 9 \)

Thus,
\[ \vec{a} + \vec{b} = 3\hat{i} + 6\hat{j} + 9\hat{k} \]

### Step 3: Subtract vector \( \vec{c} \)
Now, we need to subtract \( \vec{c} \) from \( \vec{a} + \vec{b} \):
\[ \vec{a} + \vec{b} - \vec{c} = (3\hat{i} + 6\hat{j} + 9\hat{k}) - (3\hat{i} + 6\hat{j} + 9\hat{k}) \]

### Step 4: Perform the subtraction
Subtract the corresponding components:
- \( \text{x-component: } 3 - 3 = 0 \)
- \( \text{y-component: } 6 - 6 = 0 \)
- \( \text{z-component: } 9 - 9 = 0 \)

Thus,
\[ \vec{a} + \vec{b} - \vec{c} = 0\hat{i} + 0\hat{j} + 0\hat{k} \]

### Final Result
The components of the vector \( \vec{a} + \vec{b} - \vec{c} \) are:
\[ \vec{a} + \vec{b} - \vec{c} = \vec{0} \]