Final answer:
The distance from the point (2, 1, -1/2) to the plane x + 2y + 6z = 10 is calculated by using the point-to-plane distance formula, resulting in a distance of 9 / √41.
Step-by-step explanation:
To find the distance from a point to a plane, we can use the formula for the distance of a point (x0, y0, z0) from the plane ax + by + cz + d = 0, which is given by:
|ax0 + by0 + cz0 + d| / √(a2 + b2 + c2)
Given the line x = 2, y = 1, z = -1/2, we take this as our point (x0, y0, z0), and given the equation of the plane x + 2y + 6z = 10, we identify a=1, b=2, and c=6.
The formula simplifies to:
|(1)(2) + (2)(1) + (6)(-1/2) + (-10)| / √(12 + 22 + 62)
|2 + 2 - 3 - 10| / √(1 + 4 + 36)
|-9| / √41
So, the distance is 9 / √41.