Prove that the plane `vecr*(hati+2hatj-hatk)=3` contains the line `vecr=hati+hatj+lamda(2hati+hatj+4hatk).`

Explanation

To prove that the plane \(\vec{r} \cdot (\hat{i} + 2\hat{j} - \hat{k}) = 3\) contains the line \(\vec{r} = \hat{i} + \hat{j} + \lambda(2\hat{i} + \hat{j} + 4\hat{k})\), we will substitute the parametric equation of the line into the equation of the plane and verify if it holds true.

### Step 1: Write the equation of the line
The line can be expressed as:
\[ \vec{r} = \hat{i} + \hat{j} + \lambda(2\hat{i} + \hat{j} + 4\hat{k}) \]
This can be rewritten as:
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