Q. 2 TF
Question
Explain why a single nonzero vector and a point uniquely determine a plane containing the point. (Hint: Think of the collection of vectors orthogonal to the given vector with the given point as the initial point of all of the vectors.)
Step-by-Step Solution
Verified Answer
A single nonzero vector and a point uniquely determine a plane containing the point if a given vector is a orthogonal to a plane.
1Step 1. Given Information
Explain why a single nonzero vector and a point uniquely determine a plane containing the point.
2Step 2. A nonzero vector is one whose magnitude is greater than zero.
If a given vector is orthogonal to a plane, a single nonzero vector and a point uniquely identify a plane containing the point.
If two vectors are perpendicular to each other, they are orthogonal. The dot product of the two vectors, in other words, is zero.
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