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## Homework Statement

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)

Then

**PQ**= (9, -6, 4) and

**PR**= (14, -7, 7)

The normal to the plane W2 is then

**PQ**x

**PR**= (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