Question

Find the area (with two decimal digits after the point, e.g

12.13) of the parallelogram that has the vectors U=<3,-1,5>
and V=<2,-4,1>as adjacent sides.

Answer 1

The area of the parallelogram formed by the vectors U=<3,-1,5> and V=<2,-4,1> is approximately 26.63.

Step-by-step explanation:

To find the area of the parallelogram formed by the vectors U=<3,-1,5> and V=<2,-4,1>, we need to find the magnitude of the cross product of these vectors.

1. Calculate the cross product of U and V: U x V = (3*-4 - (-1*2), -(5*2) - (3*1), (3*-4) - (-1*2)) = (-14, -11, -14)
2. Find the magnitude of the cross product: |U x V| = sqrt((-14)^2 + (-11)^2 + (-14)^2) = sqrt(392 + 121 + 196) = sqrt(709) ≈ 26.63
3. Round the area to two decimal places: Area ≈ 26.63