Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §11.2 Planes and Projections, #13 · Multivariable Calculus · Vectors & geometry

Explain why a plane cannot (a) contain … and … and be…

Explain why a plane cannot
(a) contain $(1, 2, 3)$ and $(2, 3, 4)$ and be perpendicular to $N = i + j$
(b) be perpendicular to $N = i + j$ and parallel to $V = i + k$
(c) contain $(1, 0, 0), (0, 1, 0), (0, 0, 1)$ , and $(1, 1, 1)$
(d) contain $(1, 1, - 1)$ if it has $N = i + j - k$ (maybe it can)
(e) go through the origin and have the equation $a x + b y + cz = 1$ .

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §11.2 Planes and Projections, #13

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