Final answer:
To find the area of a parallelogram formed by vectors A=2i-j and B=i+2j-3k, calculate the magnitude of their cross product, which results in √62 square units.
Step-by-step explanation:
To calculate the area of a parallelogram formed by the vectors A=2i-j and B=i+2j-3k, we use the cross product (also known as the vector product).
The area is given by the magnitude of the cross product of the two vectors.
The cross product of vectors A and B is A × B = (2i-j) × (i+2j-3k). This equals:
i-component:
(1)(-3) - (-1)(2)
= -3 + 2
= -1
j-component:
(2)(-3) - (2)(2i)
= -6 - 0
= -6
k-component:
(2)(2) - (-1)(1)
= 4 + 1
= 5
Therefore, A × B = -i - 6j + 5k.
To find the magnitude, we calculate
|A × B| = √((-1)^2 + (-6)^2 + (5)^2)
= √(1 + 36 + 25)
= √62.
Thus, the area of the parallelogram is √62 square units.