Explanation

(d)
Let $A(1,\ 0,\ - 1),\ B( - 1;2,\ 2)$
Direction ratios of segment $AB$ are $< 2,\ - 2,\ - 3 >$
$\cos\theta = \frac{\left| 2 \times 1 + 3( - 2) - 5( - 3) \right|}{\sqrt{1 + 9 + 25}\sqrt{4 + 4 + 9}} = \frac{11}{\sqrt{17}\sqrt{35}} = \frac{11}{\sqrt{595}}$
Length of projection $= (AB)\sin\theta$
$= \sqrt{(2)^{2} + (2)^{2} + (3)^{2}} \times \sqrt{1 - \frac{121}{595}}$
$= \sqrt{17}\frac{\sqrt{474}}{\sqrt{17}\sqrt{35}} = \sqrt{\frac{474}{35}}\ \ units$