Answer
i) If $u\ne-1$ then we have a line in 4-dimensional space.
ii) If $u= -1$ then we have a dot in 4-dimensional space.
Work Step by Step
Let,
$u+v+w+z=6$ .............................$(1)$
$u+w+z=4$ .............................$(2)$
$u+w=2$ .............................$(3)$
Now, Subtract $(3)$ from $(2)$, $(2)$ from $(1)$ we get,
$v+z=4$ .............................$(4)$
$z=2$ .............................$(5)$
$u+w=2$ .............................$(6)$
similarly from equation $(4),(5)$ we get,
$v=2$ .............................$(7 )$
From above equations only equation $(6)$ is dependent.
Hence, we can say that it is 4-dimensional space line.
Now, put $u= -1$ in equation $(7 )$ we get,
$u= -1$
$v=2$
$w=3$
$z=2$ and it is a dot in 4-dimensional space.
