Question

the lines l and m have vector equations.r=i+j+k+s(i-j+2k) and r=4i+6j+k+t(2i+2j+k) respectively. show that l and m intersect.

Answer 1

r=(1+s)i+(1-s)j+(1+2s)k
r=(4+2t)i+(6+2t)j+(1+t)k
Equate both the equations
(1+s)i+(1-s)j+(1+2s)k=(4+2t)i+(6+2t)j+(1+t)k
nw equating the coefficients since i,j,k are linearly independent
1+s=4+2t-(1)
1-s=6+2t-(2)
1+2s=1+t-(3)
solve (1) and (2) to get the value of s and t.
then apply the values of s and t in (3) and see if they satisfy the equation.
If they satisfy then l and m intersect.
See if u can do.

Answer 2

can u do?