Answer:
- Q is closest to the xz-plane
- R belongs to the yz-plane
Explanation:
since the xz plane represents all the points (x,0,z), then for a point (x,y,z) the distance is the absolute value of the y coordinate (see note below)
- distance from P to xz plane = P(6,2,3) = |2|=2
- distance from Q to xz plane =Q(-5,-1,4) = |-1|=1
- distance from R to xz plane = R(0,3,8) = |3|=3
then Q is closest to the xz-plane
since the yz-plane represents all the points (0,y,z) then the only point that can satisfy this condition (x=0) is R(0,3,8). Thus R belongs to the yz-plane .
Note:
if we make a vector v from the point to the (x,y,z) to the xz plane (x,0,z) :
v=(x,y,z)-(x,0,z) = (0,y,0)
then the distance will be the modulus of this vector
distance= |v|=√(0²+y²+0²)= √(y²) = |y|