Find the equation of the plane passing through the line of intersection of the planes

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asked Jan 25, 2018 in Mathematics by sforrest072 (157,439 points) 61 410 949
edited Mar 7, 2018 by Vikash Kumar

Find the equation of the plane passing through the line of intersection of the planes

vector r.(i+j+k)=1 and vector r.(2i+3j-k)+4=0 and parallel to x-axis.

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answered Jan 25, 2018 by mdsamim (213,225 points) 5 10 15
selected Jan 25, 2018 by sforrest072
 
Best answer

The given planes are

The equation of any plane passing through the line of intersection of these planes is

Its direction ratios are (2λ + 1), (3λ + 1), and (1 − λ).
The required plane is parallel to x-axis. Therefore, its normal is perpendicular to x-axis.
The direction ratios of x-axis are 1, 0, and 0.

Therefore, its Cartesian equation is y − 3z + 6 = 0
This is the equation of the required plane.

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