Answer:
r(t) and s(t) are parallel.
Step-by-step explanation:
Given that :
the lines represented by the vector equations are:
r(t)=⟨1−t,3+2t,−3t⟩
s(t)=⟨2t,−3−4t,3+6t⟩
The objective is to determine if the following lines represented by the vector equations below intersect, are parallel, are skew, or are identical.
NOTE:
Two lines will be parallel if
here;
Thus;
∴
Hence, we can conclude that r(t) and s(t) are parallel.
The ratio of the area of region R to the area of region S is:
The sides of R are in the ratio : 2:3
Let the length of R be: 2x
and the width of R be: 3x
i.e. The perimeter of R is given by:
( Since, the perimeter of a rectangle with length L and breadth or width B is given by:
)
Hence, we get:
i.e.
Also, let " s " denote the side of the square region.
We know that the perimeter of a square with side " s " is given by:
Now, it is given that:
The perimeters of square region S and rectangular region R are equal.
i.e.
Now, we know that the area of a square is given by:
and
Hence, we get:
and
i.e.
Hence,
Ratio of the area of region R to the area of region S is:
Step-by-step explanation:
from above figure calculate from the calculator and the right answer will be .....
