Verify that the points are the vertices of a parallelogram, and then find its area. (1, 1, 1), (2, 3, 2), (4, 6, 5), (5, 8, 6) STEP 1: Compute the following two vectors. (2, 3, 2) – (1, 1, 1) = (1,2,1) (5, 8, 6) – (4, 6, 5) = (1,2,1) Are these two vectors equal? Yes O No STEP 2: Compute the following two vectors. (4, 6, 5) – (1, 1, 1) = (3,5,4) (5, 8, 6) – (2, 3, 2) = (3,5,4) Are these two vectors equal? Yes O 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.

Verify that the points are the vertices of a parallelogram, and then find its area. (1, 1, 1), (2, 3, 2), (4, 6, 5), (5, 8, 6) STEP 1: Compute the following two vectors. (2, 3, 2) – (1, 1, 1) = (1,2,1) (5, 8, 6) – (4, 6, 5) = (1,2,1) Are these two vectors equal? Yes O No STEP 2: Compute the following two vectors. (4, 6, 5) – (1, 1, 1) = (3,5,4) (5, 8, 6) – (2, 3, 2) = (3,5,4) Are these two vectors equal? Yes O 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.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.

Question

Verify that the points are the vertices of a parallelogram, and then find its area.
(1, 1, 1), (2, 3, 2), (4, 6, 5), (5, 8, 6)
STEP 1: Compute the following two vectors.
(2, 3, 2) – (1, 1, 1) = (1,2,1)
(5, 8, 6) – (4, 6, 5) = (1,2,1)
Are these two vectors equal?
O Yes
O No
STEP 2: Compute the following two vectors.
(4, 6, 5) – (1, 1, 1) = (3,5,4)
(5, 8, 6) – (2, 3, 2) = (3,5,4)
Are these two vectors equal?
Yes
O 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.

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