Question

You are given the following points: A=(−6,−5,18)A=(−6,−5,18), B=(−17,0,−1)B=(−17,0,−1), C=(7,−11,−20)C=(7,−11,−20). 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

Answer:

See answer below

Step-by-step explanation:

Since the yz-plane represents all the points (0,y,z) , then the distance of any point (x,y,z) to the yz-plane is given by the difference vector

d= (x,y,z) - (0,y,z) = (x,0,0)

then the distance |d| is

|d|=√ ( x² + 0²+0²) = |x|

then the distance only depends on |x|. Therefore A has the minimum distance to the plane and its distance dA is

dA=|xA| =|-6| = 6

Similarly , the xy- plane represents all the points (x,y,0). Doing the same procedure , the distance is |z| . Then the point that is closest to this plane is B because

dB=|zB| =|-1| = 1

Also , for a point to lie in the xz-plane , has to be of the form (x,y,0) , that is zB=0 ( distance to the plane =0). Since neither A , B or C comply , then any of the points lie in this plane