Answer:
the area of the parallelogram with adjacent sides a=[1, 1, -2] and b=[3, 3, -1] is approximately 10.2956 square units.
Explanation:
To calculate the area of a parallelogram, we can use the formula: Area = magnitude of the cross product of the adjacent sides.
Given the adjacent sides:
a = [1, 1, -2]
b = [3, 3, -1]
We can calculate the cross product of a and b to find the area.
1. Calculate the cross product of a and b:
Cross product = [a2 * b3 - a3 * b2, a3 * b1 - a1 * b3, a1 * b2 - a2 * b1]
= [1 * (-1) - (-2) * 3, (-2) * 3 - 1 * 3, 1 * 3 - 1 * 3]
= [-1 + 6, -6 - 3, 3 - 3]
= [5, -9, 0]
2. Find the magnitude of the cross product:
Magnitude = sqrt(5^2 + (-9)^2 + 0^2)
= sqrt(25 + 81 + 0)
= sqrt(106)
≈ 10.2956
Therefore, the area of the parallelogram with adjacent sides a=[1, 1, -2] and b=[3, 3, -1] is approximately 10.2956 square units.