Hi,
Suppose OR meets AB at X. Then OX = mu OR, where OX and
OR are vectors.
X, A, and B are collinear, so OX = lambda
a + (1 - lambda) b for some value
of lambda.
Now lambda a + (1 - lambda)
b = mu (3 a + 5
b), from which lambda and mu can be found.
Equation of line 1 is expressed in vector form, i.e.,
r = a + lambda
d, where
r represents the position vector of a
general point on line 1,
a represents the position vector of a
specific point on line 1,
and d represents the direction
vector.
We could compare this form with our familiar equation of
a line in two-dimensional space, i.e., y = mx + c. This line passes
through the y-intercept (a specific point) and has gradient m
(quite similar to the direction vector). In vector form, we will
obtain
r = (0, c) + lambda (a, b), where b/a =
m.
Equation of line 2 is expression in cartesian form, which
can be converted to the vector form and vice-versa. Line 2 passes
through the point (1, 3, 2) and has direction vector (0, -4,
3).
Thanks.
Cheers,
Wen Shih
