1. How close does the plane \(2x+y-2z=9\) come to the origin?
2. What’s the shortest distance from the point \(\bigl(0,11,-1\bigr)\) to the plane \(2x-9y+6z=16?\)
3. Which of the points \((-16,8,12)\) or \((7,11,-10)\) or \((10,10,10)\) is closest to the plane \(-3x+7y+z=19?\)
4. How close does the line \(\bigl\langle 2,-4,3 \bigr\rangle t + \bigl(-1,6,-1\bigr)\) come to the origin?
5. What’s the shortest distance from the point \(\bigl(4,-1,-6\bigr)\) to the line \({\bigl\langle 1,0,-2 \bigr\rangle t + \bigl(0,3,13\bigr)?}\)
6. Which of the points \((6,-7,8)\) or \((1,-8,2)\) or \((-2,-7,-1)\) is closest to the line \({\bigl\langle 3,1,2 \bigr\rangle t + \bigl(9,-4,9\bigr)?}\)
7. What’s the shortest distance between the line \({\bigl\langle -1,4,1 \bigr\rangle t + \bigl(1,5,2\bigr)}\) and the \(z\)-axis?
8. What’s the shortest distance between the lines \({\bigl\langle 4,2,3 \bigr\rangle t + \bigl(-6,5,-6\bigr)}\) and \({\bigl\langle 4,2,3 \bigr\rangle t + \bigl(5,-3,4\bigr)}?\)
9. What’s the shortest distance between the lines \({\bigl\langle 0,1,3 \bigr\rangle t + \bigl(-2,8,0\bigr)}\) and \({\bigl\langle -4,-1,0 \bigr\rangle t + \bigl(-3,-6,1\bigr)}?\)