Find a vector whose length is 3 and which is perpendicular to the vector ` vec a=3 hat i+ hat j-4 hat k\ a n d\ vec b=6 hat i+5 hat j-2 hat kdot`

Explanation

To find a vector whose length is 3 and which is perpendicular to the vectors \(\vec{a} = 3\hat{i} + \hat{j} - 4\hat{k}\) and \(\vec{b} = 6\hat{i} + 5\hat{j} - 2\hat{k}\), we can follow these steps:

### Step 1: Calculate the Cross Product \(\vec{a} \times \vec{b}\)

The cross product of two vectors \(\vec{a}\) and \(\vec{b}\) gives a vector that is perpendicular to both. The formula for the cross product in determinant form is:

\[
\vec{a} \times \vec{b} = \begin{vmatrix}
...