Final answer:
To find the area of a parallelogram with given vectors as adjacent sides, use the cross product of the vectors and multiply it by the height of the parallelogram.
Step-by-step explanation:
To find the area of a parallelogram with the given vectors as adjacent sides, we can use the cross product of the two vectors. The cross product of two vectors A and B in three-dimensional space is given by the formula |A x B| = |A||B|sin(theta), where |A| and |B| are the magnitudes of the vectors and theta is the angle between them.
Once we have the magnitude of the cross product, we can find the area of the parallelogram by multiplying the magnitude by the height of the parallelogram. The height can be found by taking the magnitude of one of the vectors and multiplying it by the sine of the angle between the vector and the cross product (theta).
So, the formula for the area of a parallelogram with adjacent sides represented by vectors A and B is:
Area = |A x B| = |A||B|sin(theta).