Find the area of a parallelogram with the following.

Question

We are given the vectors AB=m+2n, AD=m-3n. Where |m|=2, |n|=3 and $\angle(m,n)=\dfrac{\pi}{6}$. Find the area of the Parallelogram.

Answer 1

Hints:

• The area of Parallelogram is the cross-product of their vectors. Thus, $AB\times AD$
• Distributive over the addition: $A\times (B+C)=(A\times B)+(A\times C)$
• Cross products of a vector with itself is $0$. Therefore, $m\times m$ and $n\times n$ is equal to $0$
• And the last one $A\times B=|A||B|sin\theta$ (where $\theta$ is the angle between $A$ and $B$)

These hints are enough to solve this problem.

Answer 2

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