The number of vectors of unit length perpendicular to the vectors `veca=2hati+hatj+2hatkandvecb=hatj+hatk` is

Options

A. one
B. two
C. three
D. infinite

Explanation

To solve the problem of finding the number of unit vectors that are perpendicular to the vectors \(\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}\) and \(\vec{b} = \hat{j} + \hat{k}\), we can follow these steps:

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

The first step is to compute the cross product \(\vec{a} \times \vec{b}\). The cross product of two vectors gives a vector that is perpendicular to both.

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