The area of the parallelogram PQRS with vertices $P = ( 0,1,1 ) , Q = ( 2,0 , - 4 )$ and $R = ( - 3 , - 2,1 )$ is

A) $3 \sqrt { 77 }$
B) $3 \sqrt { 67 }$
C) $3 \sqrt { 57 }$
D) $3 \sqrt { 58 }$
E) $3 \sqrt { 59 }$

Question

The area of the parallelogram PQRS with vertices $P = ( 0,1,1 ) , Q = ( 2,0 , - 4 )$ and $R = ( - 3 , - 2,1 )$ is

A) $3 \sqrt { 77 }$
B) $3 \sqrt { 67 }$
C) $3 \sqrt { 57 }$
D) $3 \sqrt { 58 }$
E) $3 \sqrt { 59 }$

Quizplus · Accepted Answer

The area of the parallelogram is given by the magnitude of the cross product of vectors $\overrightarrow{PQ}$ and $\overrightarrow{PR}$. Calculating these vectors and their cross product gives a magnitude of $3 \sqrt{59}$.

The Area of the Parallelogram PQRS with Vertices P=(0,1,1),Q=(2,0,−4)P = ( 0,1,1 ) , Q = ( 2,0 , - 4 )P=(0,1,1),Q=(2,0,−4)

The Area of the Parallelogram PQRS with Vertices $P = ( 0,1,1 ) , Q = ( 2,0 , - 4 )$