(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find an equation for the plane W2 through the point P(2,3,-1) containing L

[L = (3,-1,0) + t(5/3, -1/3, 1)]

2. The attempt at a solution

Let Q and R be two points on L where t = 3 and t = 6 respectively

(t = 3) Q(11, -3, 3)

(t = 6) R(16, -4, 6)

ThenPQ= (9, -6, 4) andPR= (14, -7, 7)

The normal to the plane W2 is then

PQxPR= (14, -7, 21)

Finally

W2 : a(x - x0) + b(y - y0) + c(z - z0) = 0

14(x - 2) - 7(y - 3) + 21(z - +1) = 0

14x -7y +21z + 14 = 0

Could someone please be so kind as to check my calculations (especially for the two points Q and R, I'm not sure if I derived them correctly from the line's equation)? I'm not sure if my answer is correct since I can't find any similar examples in my textbook so I'd just like to know if my reasoning is sound.

Thanks in advance.

phyz

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# Equation of plane through point P containing line L

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