False Need Help? Watch Talk to a Tutor Read It -14 points SCalc7 12 5016 (a) Fin

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False Need Help? Watch Talk to a Tutor Read It -14 points SCalc7 12 5016 (a) Find parametric equations for the line through (4, 1, 6) that is perpendicular to the plane x-y + 3z = 3, (Use the parameter t.) (xto, ye), ze)- ( (b) In what points does this line intersect the coordinate planes? xy-plane (x,y, z)- yz-plane (x, y, z)= xz-plane (x, y, z) Need Help? Talk to a Tutor 02/2 points Previous Answers SCalct 12.5 019 Determine whether the lines L1 and 42 are parallel, skew, or intersecting. Li: x = 12 + 8t, y=16-4t, z=4+12t

Explanation / Answer

Perpe to plane
As in the normal vector

Botice plane is x - y + 3z = 3

So, the normal vector of plane can be given
by direction vector
n = <1 , -1 , 3>

And point is (4,1,6)

So, parametric line is :
r = point + t*direction

r(t) = (4,1,6) + t<1,-1,3>

r(t) = <4 + t , 1 -t , 6 +3t> --> first ans

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xy plane :
Put z = 0
6 + 3t = 0
t = -2
So, <4-2 , 1 + 2 , 0>
(2 , 3 , 0) ---> ANS

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yz plane :
Put x = 0
4 + t = 0
t = -4

And thus r(t) = <4 + t , 1 -t , 6 +3t>
becomes
(0 , 5 , -6) --> ANS

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xz plane :
Put y = 0
1 - t = 0
t = 1

So, r(t) = <4 + t , 1 -t , 6 +3t>
becomes
(5 , 0 , 9) ---> ANS

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