Area of Parallelogram

Geometry Level pending

If A B → = 3 i ^ + 2 j ^ − k ^ \large \overrightarrow { AB } =3\hat { i } +2\hat { j } -\hat { k } and A D → = 5 i ^ − j ^ + 2 k ^ \large \overrightarrow { AD } =5\hat { i } -\hat { j } +2\hat { k } then what is the area of the parallelogram taking A B AB and A D AD as adjacent sides?

  • Wright the answer upto four decimal.


The answer is 17.2916.

Md Mehedi Hasan by Md Mehedi Hasan , 22, Bangladesh

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1 solution

Md Mehedi Hasan
Nov 16, 2017

Here A B → × A D → = ∣ i ^ j ^ k ^ 3 2 − 1 5 − 1 2 ∣ = 3 i ^ − 11 j ^ − 13 k ^ \overrightarrow {AB}\times\overrightarrow{AD}=\left| \begin{matrix} \hat { i } & \hat{j} & \hat{k} \\ 3 & 2 & -1 \\ 5 & -1 & 2 \end{matrix} \right| =3\hat i-11\hat j-13\hat k

So the area is = ∣ A B → × A D → ∣ = ( 3 ) 2 + ( − 11 ) 2 + ( − 13 ) 2 = 299 ≈ 17.2916 =\left| \overrightarrow{AB}\times\overrightarrow{AD}\right|=\sqrt{(3)^2+(-11)^2+(-13)^2}=\sqrt{299}\approx\boxed{\color{#3D99F6}17.2916}

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