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The position vectors of the points A and B are (1,4,6) and (3,4,7), re- spectively. Find the vector equation of the line AB and find the points where the line intersects the coordinate planes.

The answer for the first part corresponds to (1,4,6) +t(2,0,1).However i cant figure out the answer for the second part.

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First note that the equation is NOT $(1,4,6) +t(2,0,1)$, because this is not an equation. The equation is $$(x,y,z)=(1,4,6) +t(2,0,1)\ .$$ One of the coordinate planes is given by $z=0$. Using this together with the equation of the line you can find the corresponding value of $t$ and then this gives you the point of intersection. Do the same for the other coordinate planes.

Please try it for yourself now.

Hint. One of the other cases is going to end up a bit differently.

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