calculus helppp

Question

You are given the following points: 𝐴=(13,11,−20)A=(13,11,−20), 𝐵=(−16,0,10)B=(−16,0,10), 𝐶=(−9,16,16)C=(−9,16,16). 

Which point is closest to the yz-plane?

What is the distance from the yz-plane to this point?  

Which point is farthest from the xy-plane?  ? 

What is the distance from the xy-plane to this point?  

Which point lies on the xz-plane?

Answer 1

The projection of point A onto the plane yz plane is the point (0 , 11 , -20 ) ; the distance from this point to point A is |13| = 13

Similarly for point B, the distance is |16| = 16

And for point C , the distance is |-9| = 9

So point C is the closest and point B is the most distant

Point B is in the xz plane because its y component is 0

Answer 2

𝐴=(13,11,−20) 𝐵=(−16,0,10)  𝐶=(−9,16,16)

Which point is closest to the yz-plane? C

What is the distance from the yz-plane to this point?  -9 

Which point is farthest from the xy-plane?  A

What is the distance from the xy-plane to this point? -20 

Which point lies on the xz-plane? B

Answer 3

A point's distance from the yz-plane is simply the absolute value of its x-coordinate. (Analogous definitions apply to distance from the xy-plane, etc.)

So, for example, the definition of the xz-plane is the set of all points in R³ such that y = 0 (which should help you answer the last question).