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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 .