Concept explainers
Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. The plane passing through the point (1, 1, 1) with a normal
b. The equations x + y – z = 1 and – x – y + z = 1 describe the same plane.
c. Given a plane Q, there is exactly one plane orthogonal to Q.
d. Given a line l and a point P0 not on l, there is exactly one plane that contains l and passes through P0.
e. Given a plane R and a point P0, there is exactly one plane that is orthogonal to R and passes through P0.
f. Any two distinct lines in ¡3 determine a unique plane.
g. If plane Q is orthogonal to plane R and plane R is orthogonal to plane S, then plane Q is orthogonal to plane S.
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Calculus: Early Transcendentals (2nd Edition)
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