Find the points where the line given by x=7t+9, y=8t−7, and z=−7t−2 intersect the xy, xz, and yz planes.Attempted solution:This seems as though a very simple problem to me. Take, for example, finding the intersection with the xz plane. It must be that y=0. I substitute y=0 to obtain t = 7 8 , then x = 121 8 and z = − 65 8 . The point of intersection is ( 121 8 , 0 , − 65 8 )It seems, however, that my solution is wrong, which completely baffles me.What is the correct approach?

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Find the points where the line given by  x=7t+9, y=8t−7, and z=−7t−2 intersect the xy, xz, and yz planes.Attempted solution:This seems as though a very simple problem to me. Take, for example, finding the intersection with the xz plane. It must be that y=0. I substitute y=0 to obtain   t  =      7    8  , then   x  =      121    8   and   z  =  −      65    8  . The point of intersection is   (      121    8    ,  0  ,  −      65    8    )It seems, however, that my solution is wrong, which completely baffles me.What is the correct approach?

wespee0 · Accepted Answer

Find the points where the line given by x=7t+9, y=8t−7, and z=−7t−2 intersect the xy, xz, and yz planes. Your approach is correct, You can also write the equation of line in symmetric form:            x      −      9        7    =            y      +      7        8    =            z      +      2              −      7      Now intersection of this line with xy, yz and zx is respectively :xy):   z  =  0  ⇒  x  −  9  =  −  2  ⇒  x  =  7  ,  y  +  7  =  −      16    7    ⇒  y  =  −      65    7  YZ): x=0zx): y=0

Find the points where the line given by x=7t+9, y=8t−7, and z=−7t−2 intersect the xy, xz, and yz planes.

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