Answer:
The exact area is 2*sqrt(1419) square units.
The approximate area is 75.3392 square units.
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Given Vectors:
u = -4i-9j+1k
v = -6i+1j+5k
Compute the cross product u x v to get
u x v = -46i+14j-58k
See the diagram below to see how I computed the cross product.
Note: vector cross multiplication is not commutative. This means u x v = v x u is not true in general. However, the magnitude of each result is the same. So we can say |u x v| = |v x u|.
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Now compute the magnitude of vector u x v
|u x v| = sqrt((-46)^2 + (14)^2 + (-58)^2)
|u x v| = sqrt(5676)
|u x v| = sqrt(4*1419)
|u x v| = sqrt(4)*sqrt(1419)
|u x v| = 2*sqrt(1419)
|u x v| = 75.3392 which is approximate
