Find the area of the parallelogram whose sides are given by vectors a and b. Use the cross product only. (Area of the parallelogram = a x b = a cross b)

a = [ 6,3,4], b = [ 2, 5, 1]

9514 1404 393

  √869 ≈ 29.48 square units

Step-by-step explanation:

The vector cross product is ...

  (3·1 -5·4, -6·1 +2·4, 6·5 -2·3) = (-17, 2, 24)

The area is the magnitude of this vector, so is ...

  √((-17)² +2² +24²) = √(289 +4 +576) = √869 ≈ 29.48

The area is about 29.48 square units.

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