# Question:Equation of a plane (2)

## Question:Equation of a plane (2)

Write the equation for the plane P contains the straight line

d: x = 2 + t, y = t, z = 2 + 2t,

so that, the distance  from point A(2; 5; 3)  to P is maximum.

My idea.

Let K and H  be projection of the point A on the plane P and the line d, respectively. We have AK <= AH. Thus, distance from A to P reaches the maximum value if and only H coincides with K, and then P through the point K and having AH as its normal vector.

This is my code.

> with(geom3d);

`> point(A,2,5,3);                               > line(d,[1 + 2*t,t,2+2*t],t);                               > coordinates(projection(H,A,d));                          > dsegment(AH,A,H);                                > plane(P,[H,AH]);                            > Equation(P,[x,y,z]);`
`Note that P is the plane containing the straight line d and perpendicular to the plane created by point A and the line d.`
`Please comment about my code. Thank you very much.`
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