Gfind the point on the plane x + 4y + 2z =14 closest to the point (1,1,1)

(4/3, 7/3, 5/3)

Step-by-step explanation:

The line perpendicular to the plane through the point will be ...

... (x, y, z) = (1, 1, 1) +t(1, 4, 2)

Using this expression for (x, y, z), we can find the point on the line where it intersects the plane. That point is the one of interest.

... (1 +t) +4(1 +4t) +2(1 +2t) = 14 . . . . . substituting for (x, y, z) in the equation of the plane

... 7 +21t = 14 . . . . . collect terms

... 21t = 7 . . . . . . . . subtract 7

... t = 7/21 = 1/3  . . . divide by 21

The point of interest is ...

... (x, y, z) = (1, 1, 1) + (1/3)(1, 4, 2) = (1 1/3, 2 1/3, 1 2/3)

y - y1 = m(x- x1)

y - (-5) = 2/3(x -0)

y + 5 = 2/3x

y = 2/3x - 5

there has been genes found in the x chromosome of males that have been linked to [homo/hetero]sexuality. in addition to the reign of the x chromosome, a section of chromosome 8 has also been link to, "alot of ppl are so " these facts were proven true after a 2014 study of a gay male and his strait brother. according to newscientist.com,"chromosome 14 and is mainly active in the thyroid, but also the brain. called tshr, it makes a type of receptor protein that recognises and binds to a hormone that stimulates the thyroid. in this way, the gene plays an important role in controlling thyroid function. the fact that tshr seems to be involved in sexual orientation fits with evidence that thyroid function seems to be linked to sexuality."

in conclusion, "ppl are so gay" due to their genetics.