Question

Find the shortest distance from the point (1, 0, -9) to the plane x + 2y + z = 16

Answer 1

To find the shortest distance from the point (1, 0, -9) to the plane x + 2y + z = 16, we use the distance formula.

Step-by-step explanation:

To find the shortest distance from the point (1, 0, -9) to the plane x + 2y + z = 16, we can use the formula for the distance between a point and a plane. The formula is:

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

In this case, the values of A, B, C, and D are 1, 2, 1, and -16 respectively. Plugging these values into the formula, we get:

Distance = |1(1) + 2(0) + 1(-9) + (-16)| / sqrt(1^2 + 2^2 + 1^2)

Calculating this expression gives us the shortest distance from the point (1, 0, -9) to the plane x + 2y + z = 16.