Answer:
The third one
Step-by-step explanation:
consider the following image
Vocabulary// the ____ states that any # plus it's opposite equals zero
1 answer:
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Answer:
2x - y - 3z = 0
Step-by-step explanation:
Since the set
{i, j} = {(1,0), (0,1)}
is a base in
and F is linear, then
<em>{F(1,0), F(0,1)} </em>
would be a base of the plane generated by F.
F(1,0) = a+b = (2i-2j+k)+(i+2j+k) = 3i+2k
F(0,1) = a+c = (2i-2j+k)+(2i+j+2k) = 4i-j+3k
Now, we just have to find the equation of the plane that contains the vectors 3i+2k and 4i-j+3k
We need a normal vector which is the cross product of 3i+2k and 4i-j+3k
(3i+2k)X(4i-j+3k) = 2i-j-3k
The equation of the plane whose normal vector is 2i-j-3k and contains the point (3,0,2) (the end of the vector F(1,0)) is given by
2(x-3) -1(y-0) -3(z-2) = 0
or what is the same
2x - y - 3z = 0
For this case we have that by definition, the equation of a line in the point-slope form is given by:
Where:
m: It is the slope of the line and is a point through which the line passes.
We have the following equation of the slope-intersection form:
Where the slope is
By definition, if two lines are perpendicular then the product of their slopes is -1.
Thus, a perpendicular line will have a slope:
Thus, the equation will be of the form:
Finally we substitute the given point and we have:
Answer:
Option B