Practise comparing direction vectors and equating components with independent parameters to decide whether 3D lines are parallel, intersecting or skew and find an intersection.
9 Two lines l and m have equations r=3 i+2 j+5 k+s(4 i-j+3 k) and r=i-j-2 k+t(-i+2 j+2 k) respectively.
Show that l and m intersect and state the position vector of the point of intersection.
Express general point of l or m in component form,
e.g. (3+4 s, 2-s, 5+3 s) or (1-t,-1+2 t,-2+2 t)
B1
Equate at least two pairs of components and solve for s or for t
M1
Obtain correct answer s=-1 and t=2
A1
Verify that all three equations are satisfied
A1
State position vector of the intersection -i+3 j+2 k, or equivalent
A1
Can come from 1 correct value and no contradictory
statement.