Consider the vectors $\vec { u } = ( - 1,2,3 ) , \quad \vec { v } = ( 2,0 , - 1 )$ and the point $\mathrm { A } ( - 4,4,7 )$. It is requested: a) (1 point) Determine the vector $\vec { w } _ { 1 }$ that is orthogonal to $\vec { u }$ and $\vec { v }$, unitary, and with negative third coordinate. b) (0.75 points) Find the non-zero vector $\overrightarrow { w _ { 2 } }$ that is a linear combination of $\vec { u }$ and $\vec { v }$ and orthogonal to $\vec { v }$. c) (0.75 points) Determine the vertices of the parallelogram whose sides have the directions of vectors $\vec { u }$ and $\vec { v }$ and one of its diagonals is the segment $\overrightarrow { O A }$.
Consider the vectors $\vec { u } = ( - 1,2,3 ) , \quad \vec { v } = ( 2,0 , - 1 )$ and the point $\mathrm { A } ( - 4,4,7 )$. It is requested:
a) (1 point) Determine the vector $\vec { w } _ { 1 }$ that is orthogonal to $\vec { u }$ and $\vec { v }$, unitary, and with negative third coordinate.
b) (0.75 points) Find the non-zero vector $\overrightarrow { w _ { 2 } }$ that is a linear combination of $\vec { u }$ and $\vec { v }$ and orthogonal to $\vec { v }$.
c) (0.75 points) Determine the vertices of the parallelogram whose sides have the directions of vectors $\vec { u }$ and $\vec { v }$ and one of its diagonals is the segment $\overrightarrow { O A }$.