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

Question

L1: 
r= 8*i + j + s *( i + 8*j) 

L2: 
r= 6*j + t *(−5*i − 2*j)

Answer 1

Step 1:

The vector line equations are and .

Equate two lines to find the point intersection.

.

Equate terms:

.

Equate terms:

Substitute .

.

Substitute in .

.

Step 2:

Substitute in .

.

The position vector is .

Check:

Substitute in .

.

Hence the position vector obtained in two ways are same.

The position vector is .

Solution:

The position vector is .