Find the shortest distance from the point (7, 4, -6) to the plane x + y − z = 6.
I think the answer has to be in fraction form... thank you so much to whoever helps, I just can't seem to get the numbers right for it.
I think the answer has to be in fraction form... thank you so much to whoever helps, I just can't seem to get the numbers right for it.
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there is a pat formula...otherwise will give 2 ways
1st : form the function between the point and the plane ;
f(x,y) = [ x - 7]² + [ y - 4 ]² + [ x+y-6 + 6]² , minimize using partial derivatives
2nd: form the vector between the point and a point on the plane ; v = < 7 , 4 , 0 > will work
then do a scalar projection of v onto the normal vector N = < 1 , 1 , - 1 >...{ 11 / √3 }
1st : form the function between the point and the plane ;
f(x,y) = [ x - 7]² + [ y - 4 ]² + [ x+y-6 + 6]² , minimize using partial derivatives
2nd: form the vector between the point and a point on the plane ; v = < 7 , 4 , 0 > will work
then do a scalar projection of v onto the normal vector N = < 1 , 1 , - 1 >...{ 11 / √3 }