Finding a Point of IntersectionIn Exercises 33–36, determine whether the lines intersect, and if so, find the point of intersection and the angle between the lines.
To calculate: For the lines , find the point of intersection of lines if they intersect and the angle between them.
The parametric equations of the first line are:
The parametric equations of the second line are:
The angle between two lines is given by
Convert the symmetric equations of both the lines into parametric equations
This can be attained by equating the equations with and respectively.
Equations of the first line will be,
And, the equation of the second line will be
Coordinates and for both the lines will be equal at the point of intersection.
Now since, the lines intersect to each other at a point
The intersect point will be common for both the lines.
Now, equate and coordinates of both the lines. Then,
For x coordinate,
For y coordinate,
For z coordinate,
Since, by coordinate, the relation between and can be easily determined.
Form the equation (3),
Now, the value of can be determined by putting in equation (1) then,
Therefore, the value of is .
Now, with the value of , then find the value of ,
Then substitute the value of and then find the value of . Then,
Now, substitute and in the equation of first line and second line respectively. Then,
The x coordinate of for the first line is,
The y coordinate of the first line is,
The z coordinate of the first line is,
So, from the above calculation the coordinates for the first line are
Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!Get Started
Precalculus: Mathematics for Calculus (Standalone Book)
Single Variable Calculus: Early Transcendentals, Volume I
Finite Mathematics and Applied Calculus (MindTap Course List)
Calculus: Early Transcendentals
Calculus: An Applied Approach (MindTap Course List)
Calculus: Early Transcendental Functions
Essentials Of Statistics
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Calculus (MindTap Course List)
Statistics for The Behavioral Sciences (MindTap Course List)
Single Variable Calculus
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Understanding Basic Statistics
Probability and Statistics for Engineering and the Sciences
Mathematical Applications for the Management, Life, and Social Sciences
Elementary Technical Mathematics
Elementary Geometry For College Students, 7e
Mathematical Excursions (MindTap Course List)
Calculus of a Single Variable
Single Variable Calculus: Early Transcendentals
Trigonometry (MindTap Course List)
Elements Of Modern Algebra
Contemporary Mathematics for Business & Consumers
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
Calculus: Early Transcendental Functions (MindTap Course List)
Study Guide for Stewart's Multivariable Calculus, 8th
Elementary Geometry for College Students
Finite Mathematics for the Managerial, Life, and Social Sciences