Answer:
80 cm
Step-by-step explanation:
The diagonals divide the rhombus into four congruent triangles. The height of each triangle is 18/2 = 9, and the hypotenuse is 41. Using Pythagorean theorem, the width of each triangle is:
c² = a² + b²
41² = 9² + x²
x = 40
Therefore, the longer diagonal is 2×40 = 80.
The given plane has normal vector
Scaling <em>n</em> by a real number <em>t</em> gives a set of vectors that span an entire line through the origin. Translating this line by adding the vector <2, 1, 1> makes it so that this line passes through the point (2, 1, 1). So this line has equation
This line passes through (2, 1, 1) when <em>t</em> = 0, and the line intersects with the plane when
which corresponds the point (3, -1, 1) (simply plug <em>t</em> = 1 into the coordinates of ).
So the distance between the plane and the point is the distance between the points (2, 1, 1) and (3, -1, 1):
