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Find the position vector of the point of intersection of lines L1, L2 with vector equations intersecting, where;

0 votes

L1: 
r= 8*i + j + s *( i + 8*j) 

L2: 
r= 6*j + t *(−5*i − 2*j)

asked Aug 21, 2015 in PRECALCULUS by anonymous

1 Answer

0 votes

Step 1:

The vector line equations are image and image.

Equate two lines to find the point intersection.

image

image

image.

Equate image terms:

image

image.

Equate image terms:

image

Substitute image.

image

image

image

image

image

image

image.

Substitute image in image.

image

image

image

image.

Step 2:

Substitute image in image.

image

image

image

image.

The position vector is image.

Check:

Substitute image in image.

image

image

image

image.

Hence the position vector obtained in two ways are same.

The position vector is image.

Solution:

The position vector is image.

answered Aug 21, 2015 by Sammi Mentor
edited Aug 21, 2015 by Sammi

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