taiwan-gsat 2022 Q16

taiwan-gsat · Other · gsat__math-a 5 marks Vectors: Lines & Planes Find Cartesian Equation of a Plane

In coordinate space, on the plane $x - y + 2 z = 3$ there are two distinct lines $L : \frac { x } { 2 } - 1 = y + 1 = - 2 z$ and $L ^ { \prime }$ . It is known that $L$ also lies on another plane $E$ , and the projection of $L ^ { \prime }$ on $E$ coincides with $L$ . Then the equation of $E$ is $x +$ (16-1)(16-2) $y +$ (16-3)(16-4) $z =$ (16-5) .

In coordinate space, on the plane $x - y + 2 z = 3$ there are two distinct lines $L : \frac { x } { 2 } - 1 = y + 1 = - 2 z$ and $L ^ { \prime }$ .\\
It is known that $L$ also lies on another plane $E$ , and the projection of $L ^ { \prime }$ on $E$ coincides with $L$ .\\
Then the equation of $E$ is $x +$ (16-1)(16-2) $y +$ (16-3)(16-4) $z =$ (16-5) .

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