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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

vectorslinepoint-of-intersectionaskedFeb 17, 2015in CALCULUSby anonymouseditedFeb 17, 2015by steve

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.

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The point of intersection is

.