The sides of a rectangle are formed by vectors A⃗ and B⃗ with |A⃗|=2 and |B⃗|=5. Determine the area of rectangle.

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to remember that the product length multiplied by width expresses the area of rectangle.

Considering the the magnitude of vector `barA`  expresses the width and the magnitude of vector`barB ` expresses the length and since the problem provides the magnitudes of vectors `barA`  and `barB` , then you should use the following property of absolute value such that:

`|bar A|*|bar B| = |barA*barB|`

You need to substitute 2 for `|bar A|`  and 5 for `|bar B|`  such that:

Area `= |2*5| = |10|`  => Area = 10 units`^2`

Hence, evaluating the area of rectangle under given conditions yields A = 10 units`^2` .