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