Question

I got it wrong, please help me

Answer 1

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