(a) In R^2, what is the distance between the point (-1, -2) and the nearest poin
ID: 2961709 • Letter: #
Question
(a) In R^2, what is the distance between the point (-1, -2) and the nearest point in the line L defined by
2x+y = 3?
(b) What are the two coordinates of this nearest point in L?
(c) In R^3, what is the distance between the point (-1, -2, -3) and the nearest point in the plane M defined by 2x+y-z = 3 ?
(d) What are the three coordinates of this nearest point in M ?
In R^2, what is the distance between the point (-1, -2) and the nearest point in the line L defined by 2x+y = 3? What are the two coordinates of this nearest point in L? In R^3, what is the distance between the point (-1, -2, -3) and the nearest point in the plane M defined by 2x+y-z = 3 ? What are the three coordinates of this nearest point in M ?Explanation / Answer
the shortest distance between the point and the line is given by the distance between the given point and the point on the line which is the foot of the perpendicular from the point on the line
therefore the shortest distance is given by 3.13
the two coordinates of the nearest point is the foot of perpendicular from that point on that line
therefore nearest point =(9/5,-3/5) =(1.8,-0.6)
the distance between a point and a nearest point on the plane is the distance between the point and the foot of the perpendicular from that point onto that plane
therefore shortest distance =1.6393
the three coordinates of the point is the foot of perpendicular from that point onto that plane =(1/3,-4/3,-11/3)
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