Linear Math: Find a and b for Point on Line

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SUMMARY

The discussion focuses on determining the values of a and b for the point (a, b, 0) that lies on the line defined by the points (-1, -1, 6) and (-9, 7, 2). The line equation is derived using the formula L(t) = P + t*(Q-P), where P is the starting point and Q is the endpoint. The key step involves solving for the parameter t when z equals 0 and substituting this value back into the line equation to find the corresponding a and b values. The correct approach requires careful manipulation of the line equation and understanding of vector operations.

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Homework Statement




Find a and b such that the point (a,b,0) lies on the line passing through (-1,-1,6) and (-9,7,2)

Homework Equations



Basic line equations, from P to Q= Q-P..etc

The Attempt at a Solution



I keep getting the wrong answer, but I got a point at exactly P (-1,-1,6) and a direciton by doing Q-P...and solving for z=0...
 
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so the line equation is
L(t) = P + t*(Q-P)

show your work, but soudns like you're heading in the right direction, solve for t, when z=0 as you say, then substitute back into line
 

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