The vector r = xˆi + y ˆj + zkˆ, called the position vector points from the origin (0, 0, 0) to an arbitrary point in space with coordinates (x, y, z). Use what you know about vectors to prove the following: All points (x, y, z) that satisfy the equation Ax + By + Cz = 0, where A, B, and C are constants, lie in a plane that passes through the origin and that is perpendicular to the vector Aˆi + Bˆj + Ckˆ. Sketch this vector and the plane.

The vectors r and  p = Aˆi + Bˆj + Ckˆ are perpendicular between them. Thus, the plane equation come from the fact that the dot product is equal to zero.

Step-by-step explanation:

The dot product of r and p

r*p = (xˆi + y ˆj + zk)*(Aˆi + Bˆj + Ckˆ) = Ax + By + Cz = 0

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

0.84 dang lotta people are looking for this lol or if you round up its 1 but the overall answer to that is 0.84

step-by-step explanation: