lines L1 and L2 have vector equations r=8i-j+3k+λ(-4i +j)µ(i +3j - 2k) respectively. it then says show that L1 and L2 intersect and find the position vector of the point of intersection.

and r= -2i +8j - k +

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- April 5th 2010, 12:40 PMkandyflossVectors in 3D question
lines L1 and L2 have vector equations r=8i-j+3k+

**λ(-4i +j)**µ(i +3j - 2k) respectively. it then says show that L1 and L2 intersect and find the position vector of the point of intersection.

and r= -2i +8j - k + - April 5th 2010, 02:23 PMSoroban
Hello, kandyfloss!

Quote:

Lines and have vector equations: .

Show that and intersect and find the position vector of the point of intersection.

. . . .

From [9], we have: .

Substitute into [8]: .

Substitute into [1], [2] and [3]:

. .

Substitute into [4], [5] and [6]:

. .

Therefore, the lines intersect at: .

The position vector of is: .

- April 12th 2010, 10:48 AMkandyfloss
Excellent explanation!

thanks (Happy)