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Equation of a line that passes through a point. 
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#1
May2111, 09:53 PM

P: 292

1. The problem statement, all variables and given/known data
Find the equation of the line that passes through A(1,4, 2) and is parallel to the intersection line of the two planes x  2y + 3z  1 = 0 and x  4y+ 2z  8 = 0 2. Relevant equations N/A 3. The attempt at a solution First I set the first and second equations to [1] and [2]: x  2y + 3z  1 = 0 [1] x  4y+ 2z  8 = 0 [2] I then multiply [1] by 2 and use elimination to get rid of the y variable for now: 2x  4y + 6z  2 = 0 x  4y + 2z  8 = 0 ________________________ x + 4z + 6 = 0 [3] I'll then let z = t to solve for x in equation [3]: x + 4t + 6 = 0 x = 4t  6 Now I substitute z = t and x = 4t  6 into equation [1] to solve for y: 4t  6  2y + 3t  1 = 0 y = (1/2)t  7/2 Now that I have the values of all the unknowns, I first express it in parametric form: x = 4t  6 y = (1/2)t  7/2 z = t Knowing this, finally, the direction vector for the line that passes through A(1, 4, 2) can be expressed: (x,y,z) = (1, 4, 2) + t(4, 1/2, 1) I just wanted to know, did I do this correctly? I feel as if I did something wrong. If I did, can you point where I went wrong? Thank you in advance. 


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