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Find an equation of the plane.

The plane that passes through the point $ (6, -1, 3) $ and contains the line with symmetric equations $ \frac{x}{3} = y + 4 = \frac{z}{2} $

$x-y-z=4$

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Campbell University

Harvey Mudd College

Idaho State University

Boston College

Yeah. In the question they're asking to find the equation of the plane that passes through the 0.6 minus 13 and contains the line with symmetric equations. X by three were two, Y plus 40 quarters it by two, rearranging this equation and assigning this tool constant value, we can write it as X by three Is equal to Y-plus four is equal to zero x 2 is equal to T see it is equal to x equal to treaty, Then by equal to T -4 And that equal to two T. And the constant attached to these coordinates are zero minus four and zero. And the coefficients For these coordinates at three, one and 2 respectively. So a point in the plane is given, say it is called B Its value is 6 -1, 3. And another point in the plane considering no coordinates given in the question is 0 -4 and zero. That is the constant values for each of the coordinates and the normal victor passes to the point 312 in the plane. That is a coefficient of the coordinates. Now, in order to find the equation of the plane to find a line passing through the plane that they speak you which has the direction vector equal to 0 -6, icap plus minus four plus 1. Jacob Less 0 -3, Caykur, it is equal to -6. I got -3 Jacob -3. Jacob. Therefore the cross productive PQ and n victor is Ichabod Jacob, Jacob and the value of PQ is -6 -3 -3 and the value of In is 312. Mhm. Therefore the value of the cross product is equal to yeah Mhm minus three. Icap this tree Jacob Plus three K Cab. Therefore the equation of the plane is mhm. Yeah minus three X minus six. Last three Y plus one Last three. Zed -3. equal to zero considering point. Okay. Mhm. 6 -1. 3. Yeah that is given in the question. This is the point B. So this is equal to after solving the equation we get x minus y minus Z. Is equal to fool and this is the required answer. Are the given question? Yeah and they put this is the equation of the plane.