Find the distance of the point (3,4,5) from the plane x+y+z=2 measured parallel to the line 2x=y=z.

Question

Yash Jain · Answer

The answer is 6 units. I’ll give you hints.
Dr’s of the line is Therefore, PN = sqrt[(3-1)
So N = (1,0,1)
Satisfying this point on the plane gives u=-4
General point on this line is..(u/2 +3, u+4, u+5) say N
Eq. of the line passing through given point P(3,4,5) with these Dr’s (x-3)/1/2=(y-4)/1=(z-5)/1
2+(5-1)2+(4-0)2] = 6units

Yash Jain · Answer

The answer is 6 units. I’ll give you hints.
Dr’s of the line is Therefore, PN = sqrt[(3-1)
So N = (1,0,1)
Satisfying this point on the plane gives u=-4
General point on this line is..(u/2 +3, u+4, u+5) say N
Eq. of the line passing through given point P(3,4,5) with these Dr’s (x-3)/1/2=(y-4)/1=(z-5)/1
2+(5-1)2+(4-0)2] = 6units

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Find the distance of the point (3,4,5) from the plane x+y+z=2 measured parallel to the line 2x=y=z.

Find the distance of the point (3,4,5) from the plane x+y+z=2 measured parallel to the line 2x=y=z.

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