taiwan-gsat 2023 Q10

taiwan-gsat · Other · ast__math-a 6 marks Vectors 3D & Lines Line-Plane Intersection

In coordinate space, there is a line $L$ with direction vector $( 1 , - 2, 2 )$, plane $E _ { 1 } : 2 x + 3 y + 6 z = 10$, and plane $E _ { 2 } : 2 x + 3 y + 6 z = - 4$. The length of the line segment of $L$ cut off by $E _ { 1 }$ and $E _ { 2 }$ is . (Express as a fraction in lowest terms)

In coordinate space, there is a line $L$ with direction vector $( 1 , - 2, 2 )$, plane $E _ { 1 } : 2 x + 3 y + 6 z = 10$, and plane $E _ { 2 } : 2 x + 3 y + 6 z = - 4$. The length of the line segment of $L$ cut off by $E _ { 1 }$ and $E _ { 2 }$ is \underline{\hspace{2cm}}. (Express as a fraction in lowest terms)

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