Question

Find the area of parallelogram if its two sides are formed by the vectors A=2i-2j+3k and B =3i+3j+3k ?

Answer 1

Not sure if this is the best way, but I would approach it like this:

1.Find the lengths of the sides using Pythagorean theorem. This gives me 3.61 for the shorter side and 5.39 for the longer side.

2.Next find the angle between the adjacent line segments by atan(3/2) + a tan(2/5). This gives an angle of 134 degrees. (By atan, I mean inverse tan). This also means that the other interior angle is 180 - 134 = 46 degrees.

3.Find the perpendicular height by calculating 3.61 x cos(46) = 2.5.

4.The area will be 5.39 times 2.5 which is approximately 13.49 square units.

Hope it helps.