Find the area of the parallelogram.
-$\mathrm { P } _ { 1 } ( 1,2,0 ) , \mathrm { P } _ { 2 } ( - 2,3,2 ) , \mathrm { P } _ { 3 } ( 0 , - 2,3 )$
A) $\sqrt { 277 }$
B) $5 \sqrt { 17 }$
C) $\sqrt { 14 }$
D) $\sqrt { 26 }$

Question

Quizplus · Accepted Answer

The area of the parallelogram can be found using the cross product of vectors $\overrightarrow{P_1P_2}$ and $\overrightarrow{P_1P_3}$. Calculate these vectors, find their cross product, and then find the magnitude of the resulting vector. The magnitude is $5 \sqrt { 17 }$.

Find the Area of the Parallelogram P1(1,2,0),P2(−2,3,2),P3(0,−2,3)\mathrm { P } _ { 1 } ( 1,2,0 ) , \mathrm { P } _ { 2 } ( - 2,3,2 ) , \mathrm { P } _ { 3 } ( 0 , - 2,3 )P1​(1,2,0),P2​(−2,3,2),P3​(0,−2,3)

Find the Area of the Parallelogram $\mathrm { P } _ { 1 } ( 1,2,0 ) , \mathrm { P } _ { 2 } ( - 2,3,2 ) , \mathrm { P } _ { 3 } ( 0 , - 2,3 )$