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Determine whether the lines L1 and L2 are parallel, skew, or intersecting

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Determine whether the lines L1 and L2 are parallel, skew, or intersecting. If they intersect, find the point of intersection.

asked Feb 17, 2015 in CALCULUS by anonymous
edited Feb 17, 2015 by steve

2 Answers

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Step 1:

Symmetric equations of the lines are

and image.

Standard form of symmetric equations of the line are .

Here vector is parallel line to the above line.

Parallel line corresponding to the line is .

Consider .

Similarly parallel line corresponding to the line is .

Consider  .

If these two parallel lines image are parallel, then the lines and are also parallel.

Find the cross product of and .

The cross product is not equal to zero, then the lines are not parallel.

 

answered Feb 18, 2015 by cameron Mentor
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Continued:

Step 2:

Check for intersection of the  lines:

If and had a point of intersection, then find the point by solving the lines.

Consider and

Write the line equations in parametric form.

and .

Equate the corresponding values.

image

             Equation(1)

       Equation(2)

   Equation(3)

Solve equation(1) and equation(2) and find the values of and .

Multiply the equation(1) by 2.

Subtract the above two equations.

Substitute in equation(1).

substitute and in equation(3).

Thus, the values of   satisfy the equation(3).

The lines and are intersecting lines.

Substitute    in the line equation to get the point of intersection.

The point of inter section is .

Solution:

The lines and are intersecting lines.

The point of intersection is .

answered Feb 18, 2015 by cameron Mentor
edited Feb 18, 2015 by cameron

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