Where does the line through A(−3, 1, 0) and B(−1, 5, 6) intersect the plane 2x + y − z + 2 = 0? Justify all your steps

(0, 7, 9)

Step-by-step explanation:

The direction vector (a, b, c) is given by B - A

(a, b, c) =  (−1, 5, 6) - (-3, 1, 0) = (2, 4, 6)

(a, b, c) = (2, 4, 6)

Let us use point A as , therefore (-3, 1, 0) =  

Substituting the value of x, y and z into the plane equation:

2x + y − z + 2 = 0

2(-3+2t) + (1 + 4t) - (6t) + 2 = 0

-6 + 4t + 1 + 4t - 6t + 2 = 0

2t -3 = 0

2t = 3

t = 3/2

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step-by-step explanation: