Statement 1 - If x , y , z ∈ R and 3 x + 4 y + 5 z = 10 2 , then the least value of x 2 + y 2 + z 2 is 4. Statement 2 - If π is a given plane and P is a given point, then the point on the plane whic

Question

Statement 1 - If x , y , z ∈ R and 3 x + 4 y + 5 z = 10 2 ​ , then the least value of x 2 + y 2 + z 2 is 4. Statement 2 - If π is a given plane and P is a given point, then the point on the plane which is nearest to P is the foot of the perpendicular from P to the plane.

TestHub · Accepted Answer

x 2 + y 2 + z 2 is the squared distance of ( x , y , z ) from the origin, and ( x , y , z ) lies on the plane 3 x + 4 y + 5 z = 10 2 ​ . The least value is the squared perpendicular distance: ( 50 ​ 10 2 ​ ​ ) 2 = 4 . Statement 1 is true by Statement 2, which is true.

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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