Question

Verify that the points are the vertices of a parallelogram, and then find its area. (1, 1, 1), (4, 3, 6), (2, 2, 5), (5, 4, 10)

STEP 1: Compute the following two vectors. (4,3, 6) - (1, 1, 1) = (5, 4, 10) - (2, 2, 5) = Are these two vectors equal?
1) Yes
2) No
STEP 2: Compute the following two vectors. (2, 2, 5) - (1, 1, 1) (5, 4, 10) - (4, 3, 6) = Are these two vectors equal?
1) Yes
2) No
STEP 3: Compute the cross product of the two vectors from above.
STEP 4: Compute the norm of the cross product to compute the area of the parallelogram.​

Answer 1

To verify if the points form a parallelogram, compute the vectors between the points and check their equality. Then, compute the cross product of the two equal vectors and find its norm to get the area of the parallelogram.

Step-by-step explanation:

To verify if the points are the vertices of a parallelogram, we need to compute the vectors formed by the points.

Step 1: Find the vectors (4, 3, 6) - (1, 1, 1) and (5, 4, 10) - (2, 2, 5). Are these two vectors equal? Answer: No

Step 2: Find the vectors (2, 2, 5) - (1, 1, 1) and (5, 4, 10) - (4, 3, 6). Are these two vectors equal? Answer: Yes

Step 3: Compute the cross product of the two vectors from Step 2.

Step 4: Compute the norm of the cross product to find the area of the parallelogram.