Let `oversetto a=3hati+2hatj+xhatk` and `oversettob=hati-hatj+hatK`
Some real x. Then `|oversettoaxxoversettob|=r` is possible if:

A. ` 3 sqrt ((3 )/(2)) lt r lt 5sqrt ((3)/(2)) `
B. ` 0 lt r le sqrt ((3)/(2)) `
C. ` r ge 5 sqrt (( 3 )/(2)) `
D. `sqrt (( 3 ) /(2) lt r le 3 sqrt ((3 ) /(2))`

Options

A. ` 3 sqrt ((3 )/(2)) lt r lt 5sqrt ((3)/(2)) `
B. ` 0 lt r le sqrt ((3)/(2)) `
C. ` r ge 5 sqrt (( 3 )/(2)) `
D. `sqrt (( 3 ) /(2) lt r le 3 sqrt ((3 ) /(2))`

Explanation

To solve the problem, we need to find the conditions under which the magnitude of the cross product of two vectors \( \vec{a} \) and \( \vec{b} \) is equal to \( r \). Let's go through the steps systematically.

### Step 1: Define the Vectors
Given:
\[ \vec{a} = 3\hat{i} + 2\hat{j} + x\hat{k} \]
\[
...