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Consider the planes 2x + 1y + 5z = 1 and 2x + 5z = 0.

AFind the unique point P on the y-axis which is on both planes. ( ? , ? , ? )

BFind a unit vector u with positive first coordinate that is parallel to both planes.

? I + ? J + ? K

CUse the vectors found in parts (A) and (B) to find a vector equation for the line of intersection of the two planes,r(t) =

? I + ? J + ? K

Verified Answer :

syed514

B is easy, given 2x + 1y + 5z = 1 and 2x + 5z = 0, normal vectors of
those planes are (2,1,5) and (2,0,5), cross product will give the
parallel vector, divide by its length so it gives the unit vector

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