If a=<1,3,4> b=<-2,2,1> the area of the parallelogram with 2 adjacent sides formed by vectors a & b will be?

these are the possible solutions to choose from in the back of the book......








a. 12.4





b. 13.0





c. 15





d. 15.3





or none of these

If a=%26lt;1,3,4%26gt; b=%26lt;-2,2,1%26gt; the area of the parallelogram with 2 adjacent sides formed by vectors a %26amp; b will be?
b. 13.0





a.b = |a||b|cosx where x is the angle between vectors.


8 = sqrt(26).(3)cosx


x = 58.5 degrees





Area of half a parallelogram = area of triangle = (1/2)abSinC.





Area of parallelogram with unit vector sides


= 2 [(1/2)(sqrt26)(3)Sin58.5]


= 13.0
Reply:If a= %26lt;1,3,4%26gt; b= %26lt;-2,2,1%26gt; the area of the parallelogram with 2 adjacent sides formed by vectors a %26amp; b will be?





The area of a parallelogram for which we know the length of two sides, a and b, and the included angle θ is:





Area = absinθ.





The magnitude of the cross product of vectors a and b is:





| a X b | = || a || || b || sinθ





So we want the magnitude of the cross product. We don't know the angle θ directly but it is implicitly known since vectors have both magnitude and direction.





| a X b | = || %26lt;1, 3, 4%26gt; X %26lt;-2, 2, 1%26gt; || = || %26lt;-5, -9, 8%26gt; ||





| a X b | = √[(-5)² + (-9)² + 8²] = √(25 + 81 + 64) = √170





Area = √170 ≈ 13.0





The answer is b.
Reply:I am 100% sure it is d. 15.3 is correct