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Consider the plane through the points A = (0,1,1), B = (1,1,0), and C = (1,0,3), as well as lines along the plane in the directions of $$\overrightarrow{AB}$$and $$\overrightarrow{AC}$$, spaced at integer multiples of those vectors:

The vectors v and w in the picture above are parallel to the plane. What are they equal to?

b). Find the value of x such that $$\mathbf{v} = \begin{pmatrix} 1 \\ 2 \\ x \end{pmatrix}$$is a vector parallel to the plane through the points A = (0,1,1), B = (1,1,0) and \$C = (1,0,3).

c). Find the normal vectorn $$\mathbf{n} = \begin{pmatrix} n_1 \\n_2 \\ n_3 \end{pmatrix}$$ to the plane through points A = (0,1,1), B = (1,1,0) and C = (1,0,3), such that $$n_1 + n_2 + n_3 = 5.$$

d). The equation of the plane through the points A = (0,1,1), B = (1,1,0) and C = (1,0,3) can be written as ax + by + cz = 8. Then what's the ordered triple (a, b, c)?

Dec 30, 2019

#1
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b) The value of x is 5.

c) n = (3,3,-1).

Dec 30, 2019
#2
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those are both incorrect

Guest Dec 30, 2019