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Determine whether the present L1 and L2 are parallel, skew, or intersecting 0 votes

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

You are watching: Determine whether the lines l1 and l2 are parallel skew or intersecting

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vectorslinepoint-of-intersectionaskedFeb 17, 2015in CALCULUSby anonymouseditedFeb 17, 2015by steve
please log in or register to add a comment. please log in or register to price this question. 2 answers 0 votes

Step 1:

Symmetric equations of the lines are

*

and

*
.

Standard kind of symmetric equations of the line space

*
.

Here vector

*
is parallel heat to the above line.

Parallel line corresponding to the line

*
is
*
.

Consider

*
.

Similarly parallel line equivalent to the line

*
is
*
.

Consider

*
.

If these 2 parallel currently

*
room parallel, climate the present
*
and
*
are likewise parallel.

Find the cross product the

*
and also
*
.

*

The cross product is no equal to zero, then the lines space not parallel.


Continued:

Step 2:

Check because that intersection of the lines:

If

*
and also
*
had a point of intersection, then find the allude by solving the lines.

Consider

*
and
*

Write the line equations in parametric form.

*
and
*
.

Equate the corresponding values.

*

*
Equation(1)

*
Equation(2)

*
Equation(3)

Solve equation(1) and equation(2) and also find the worths of

*
and also
*
.

Multiply the equation(1) by 2.

*

*

Subtract the over two equations.

*

Substitute

*
in equation(1).

*

substitute

*
and
*
in equation(3).

*

Thus, the worths of

*
fulfill the equation(3).

The lines

*
and
*
space intersecting lines.

Substitute

*
in the line equation
*
to get the allude of intersection.

*

The allude of inter ar is

*
.

Solution:

The lines

*
and also
*
are intersecting lines.

See more: What Does Not In Bop Custody Means, What Does Not In Bop Custody Mean

The point of intersection is

*
.


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