(a.)
To Show: If
(a.)
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Answer to Problem 48E
It has been shown that, if
Explanation of Solution
Given:
The expressions;
Concept used:
The equation of the line through
Calculation:
It is given that
Simplifying,
Dividing the second equation by the first equation,
Simplifying,
As discussed, this is the equation of the line through
Conclusion:
It has been shown that, if
(b.)
To Show: The given expressions are a parametrization for the line through the points
(b.)
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Answer to Problem 48E
It has been shown that the given expressions are a parametrization for the line through the points
Explanation of Solution
Given:
The expressions;
Concept used:
The equation of the line through the points
Calculation:
It is given that
Simplifying,
Dividing the second equation by the first equation,
Simplifying,
As discussed, this is the equation of the line through the points
Conclusion:
It has been shown that the given expressions are a parametrization for the line through the points
(c.)
A parametrization for the line segment with the given end points.
(c.)
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Answer to Problem 48E
It has been determined that the parametrization for the line segment with the given end points;
Explanation of Solution
Given:
The endpoints
Concept used:
The equation of the line through the points
Calculation:
As discussed, the equation of the line through the points
Simplifying the equation,
Now, let
Then the two equations obtained are:
Simplifying,
On further simplification,
Now, put
Simplifying,
This gives
Similarly, put
Simplifying,
This gives
So, the required parametrization is;
Conclusion:
It has been determined that the parametrization for the line segment with the given end points;
Chapter 0 Solutions
CALCULUS-W/XL ACCESS
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