Question

Let p, q, and r be the vertices of a parallelogram with adjacent sides pq and pr. In each case, find the other vertex s.

a. s(1, 0, 3)
b. s(5, -5, -1)
c. s(1, -3, 0)
d. s(0, 1, 2)

Answer 1

To find the other vertex of a parallelogram with given adjacent sides, use the vector difference method.

Step-by-step explanation:

To find the other vertex of the parallelogram, we can use the given coordinates of the vertices and the fact that opposite sides of a parallelogram are equal in length.

For example (a):

Given: p(0, 0, 0), q(3, 0, 0), and r(0, 1, 0).
We know that pq and pr are adjacent sides.
Let's find the vector difference pq = q - p = (3-0, 0-0, 0-0) = (3, 0, 0).
Using the vector difference method, we can find s: s = r + pq = (0, 1, 0) + (3, 0, 0) = (3, 1, 0).