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The three points give you three equations, which you can solve by your favorite method.
.. 0m +0n +b = 6
.. 1m +0n +b = -3
.. 0m +2n +b = 5
(m, n, b) = (-9, -1/2, 6)
so the equation of the plane can be written as
.. z = -9x -1/2y +6
_____
In standard form, this would be
.. 18x +y +2z = 12
.. 0m +0n +b = 6
.. 1m +0n +b = -3
.. 0m +2n +b = 5
(m, n, b) = (-9, -1/2, 6)
so the equation of the plane can be written as
.. z = -9x -1/2y +6
_____
In standard form, this would be
.. 18x +y +2z = 12
Answer:
cos(θ) = 3/5
Step-by-step explanation:
We can think of this situation as a triangle rectangle (you can see it in the image below).
Here, we have a triangle rectangle with an angle θ, such that the adjacent cathetus to θ is 3 units long, and the cathetus opposite to θ is 4 units long.
Here we want to find cos(θ).
You should remember:
cos(θ) = (adjacent cathetus)/(hypotenuse)
We already know that the adjacent cathetus is equal to 3.
And for the hypotenuse, we can use the Pythagorean's theorem, which says that the sum of the squares of the cathetus is equal to the square of the hypotenuse, this is:
3^2 + 4^2 = H^2
We can solve this for H, to get:
H = √( 3^2 + 4^2) = √(9 + 16) = √25 = 5
The hypotenuse is 5 units long.
Then we have:
cos(θ) = (adjacent cathetus)/(hypotenuse)
cos(θ) = 3/5
