Answer:
(b) 1
Step-by-step explanation:
To differentiate we will need the product rule:
.
We have , so the following equation is true by the transitive property:
By subtraction property we have:
Since , then we can divide both sides by
:
This implies is constant.
So we have that where
is a real number.
Since and
, then by transitive property
.
So .
Checking:
So the following conditions were met.
Given:
The vertices of a parallelogram are P(1,2,1), Q(1,0,-1), R(2,2,0).
PQ and PR are the adjacent sides of the parallelogram.
To find:
The coordinates of vertex S.
Solution:
We know that, the diagonals of a parallelogram bisect each other.
Let the coordinates of the vertex S are (a,b,c).
In the given parallelogram PS and QR are the diagonals. It means their midpoints are same.
On comparing both sides, we get
Similarly,
And,
Hence, the coordinates of vertex S are (2,0,-2).