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November 10th, 2010, 07:54 AM   #1
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Line/plane problem (vectors)

A line passes through the point P (3, 4, 1) and has direction vector (1, 2, 2). The point Q is also on and lies the same distance above the plane z = 4 as P is below that plane. What are the coordinates of Q?

If P and Q are on the same line, then how can Q be above the plane and P below it? (I drew a horizontal line).
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November 10th, 2010, 01:29 PM   #2
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Re: Line/plane problem (vectors)

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Originally Posted by TsAmE
A line passes through the point P (3, 4, 1) and has direction vector (1, 2, 2). The point Q is also on and lies the same distance above the plane z = 4 as P is below that plane. What are the coordinates of Q?

If P and Q are on the same line, then how can Q be above the plane and P below it? (I drew a horizontal line).
First write out the equation for the line:
A=P + Vt, where P=(3,4,1) and V=(1,2,2)
On the plane, the z coordinate for A is given by 1 + 2t = 4, or t=1.5. To get Q, use t=3 (1.5 above) so:
Q=(6,10,7)

To answer your second question, a line in the plane z=4 would have a constant 4 for the z coordinate, i.e. the vector V would have 0 for the z coordinate and P would have 4 for the z coordinate.
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