The cartesian equations of a line are x = ay +b, z = cy + d. Find its direction ratios and
reduce it to vector form.
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Step-by-step explanation:
The cartesian equation of the given line is x=ay+b,z=cy+d It can be re-written as
a
x−b
=
1
y−0
=
c
z−d
Thus, the given line passes through the point (b,0,d) and its direction ratios are proportional to a,1,c. It is also parallel to the vector
b
=a
i
+
j
+c
k
We know
that the vector equation of a line passing through a point with position vector
a
and parallel to the vector
b
is
r
=
a
+λ
b
Vector equation of the required line is
r
=(b
i
+0
j
+d
k
)+λ(a
i
+
j
+c
k
)
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