Pls help me out... :)

Mathematics

1 answer:

Misha Larkins [42]3 years ago

7 0

Answer:I think the answer is 112

Step-by-step explanation:

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Let R = [ 0 , 1 ] × [ 0 , 1 ] R=[0,1]×[0,1]. Find the volume of the region above R R and below the plane which passes through th

Bond [772]

The three vectors $\langle0,0,1\rangle$ , $\langle1,0,8\rangle$ , and $\langle0,1,9\rangle$ each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,

$\langle1,0,8\rangle-\langle0,0,1\rangle=\langle1,0,7\rangle$

$\langle0,1,9\rangle-\langle0,0,1\rangle=\langle0,1,8\rangle$

Then the cross product of these two results is normal to the plane:

$\langle1,0,7\rangle\times\langle0,1,8\rangle=\langle-7,-8,1\rangle$

Let $(x,y,z)$ be a point on the plane. Then the vector connecting $(x,y,z)$ to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that