Question

Find the distance from point p(1, 7, −6) to the plane of equation 5x − y+4z − 8 = 0.

Answer 1

To find the distance from a point to a plane in three-dimensional space, you can use the formula: Distance = |Ax + By + Cz + D| / sqrt(A^2 + B^2 + C^2).

Step-by-step explanation:

To find the distance from a point to a plane in three-dimensional space, you can use the formula:

Distance = |Ax + By + Cz + D| / sqrt(A^2 + B^2 + C^2)

In this case, the equation of the plane is 5x - y + 4z - 8 = 0, so A = 5, B = -1, C = 4, and D = -8. The coordinates of point P are (1, 7, -6).

Plugging in these values into the formula:

Distance = |5(1) + (-1)(7) + 4(-6) + (-8)| / sqrt(5^2 + (-1)^2 + 4^2)

Distance = 12 / sqrt(42)

Therefore, the distance from point P(1, 7, -6) to the plane 5x - y + 4z - 8 = 0 is approximately 1.861 units.