Concept explainers
a.
To find: A non-zero
a.
Answer to Problem 37E
The vector
Explanation of Solution
Given:
The park is determined by a plane which contains the points
Calculation:
Let the points contains by a plane is
One of the feature of the park is a monument that must be perpendicular to the ground. To represent the monument perpendicular to the ground we have to find the non-zero vector.
The cross product of any two vector in a plane is perpendicular to the plane determined by that plane.
Hence,
Now,
Similarly,
Therefore, the vector
b.
To find: The criteria so that we know that the vector is perpendicular to the plane defining by the park.
b.
Answer to Problem 37E
The answer is shown below.
Explanation of Solution
Given:
The park is determined by a plane which contains the points
Calculation:
If two vectors are perpendicular then the dot product is zero and the cross product of any two vector is always perpendicular to both vectors and perpendicular to the plane in which these two vector lies.
Therefore, the information is given above.
Chapter 8 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
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