To find: The angle between the two adjacent sides of the tank.
Answer to Problem 61E
The angle between the two adjacent sides of the tank is
Explanation of Solution
Given information:
A company that produces after-market machine parts is designing a reproduction of a fuel tank with the shape and dimensions shown in the figure.
Calculation:
The one side of the tank is the plane passing through the points
Find the component form of the
Now find the component form of the vector
Use the cross product of vectors
Use the general equation of the plane.
Substitute
So, the general equation of the plane of the first side of the tank is
The one side of the tank is the plane passing through the points
First find the component form of the vector
Now find the component form of the vector
Use the cross product of vectors
Use the general equation of the plane.
Now substitute
So, The general equation of the plane of the first side of the tank is
Compare the equation of the plane with
So, the normal vector for plane
The angle between the two planes is equal to the angles between their normal vectors.
Use the formula for angle between two vectors
The dot product of both the vectors
Now substitute all the values in the formula for angle.
The solution for the trigonometric equation
Therefore, the angle between the two adjacent sides of the tank is
Chapter 10 Solutions
Precalculus with Limits: A Graphing Approach
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