taiwan-gsat 2025 Q6

taiwan-gsat · Other · gsat__math-a 5 marks Vector Product and Surfaces
In coordinate space, there are three mutually perpendicular vectors $\vec { u } , \vec { v } , \vec { w }$. Given that $\vec { u } - \vec { v } = ( 2 , - 1,0 )$ and $\vec { v } - \vec { w } = ( - 1,2,3 )$. What is the volume of the parallelepiped spanned by $\vec { u } , \vec { v } , \vec { w }$?
(1) $2 \sqrt { 5 }$
(2) $5 \sqrt { 2 }$
(3) $2 \sqrt { 10 }$
(4) $4 \sqrt { 5 }$
(5) $4 \sqrt { 10 }$
In coordinate space, there are three mutually perpendicular vectors $\vec { u } , \vec { v } , \vec { w }$. Given that $\vec { u } - \vec { v } = ( 2 , - 1,0 )$ and $\vec { v } - \vec { w } = ( - 1,2,3 )$. What is the volume of the parallelepiped spanned by $\vec { u } , \vec { v } , \vec { w }$?\\
(1) $2 \sqrt { 5 }$\\
(2) $5 \sqrt { 2 }$\\
(3) $2 \sqrt { 10 }$\\
(4) $4 \sqrt { 5 }$\\
(5) $4 \sqrt { 10 }$