Given
a
= (1,0,0) the vector equation for the line is
$$\mathbf{x} = \mathbf{a} + \lambda \mathbf{b}$$
$$(x, y, z) = (1,0,0) + \lambda (0,1,1)$$
Which is equivalent to the scalar equations:
$$x = 1$$
$$y = \lambda$$
$$z = \lambda$$
Using algebra to eliminate λ from the last two equations, we obtain
y = z
.
Thus the Cartesian equations are
$$x = 1$$
$$y = z$$
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