Question

Use the given points to answer the following questions. A(−2, 0, −6), B(4, 2, −5), C(1, 3, 2) Which of the points is closest to the yz-plane? A B C Which point lies in the xz-plane? A B C

Answer 1

Answer:

the point C is closest to the yz-plane but any of the 3 points lie on this plane

Step-by-step explanation:

the distance of any point (x,y,z) to the yz-plane (0,y,z) is the modulus of the vector d,such that

d= (x,y,z)-  (0,y,z) = (x,0,0)

then

|d|= √(x²+0²+0²)= |x|

then the distance is given by the x coordinate of the points

for

A(−2, 0, −6) → |d| = |-2| = 2

B(4, 2, −5)  → |d| = |4| = 4

C(1, 3, 2) → |d| = |1| = 1

then the point C is closest to the  yz-plane

a point lies on the yz-plane of the distance to it is 0 (|d|=|x|=0) , then any of the 3 points lie on this plane.