The length of projection, of the line segment joining the points (1, -1, 0) and (-1, 0, 1), to the plane 2x + y + 6z = 1, is equal to :

$\sqrt{\frac{237}{61}}$

Let A = (1, –1, 0), B = (–1, 0, 1)

Direction rations of segment AB are

2, –1, –1

If ‘θ’ be the acute angle between segment AB and normal to plane,

$\cos \theta=\frac{|2.2-1.1-1.6|}{\sqrt{4+1+36} . \sqrt{4+1+1}}=\frac{3}{\sqrt{246}}$

Length of projection

= (AB) sin θ

$=\sqrt{6} . \sqrt{1-\frac{9}{246}}=\sqrt{\frac{237}{61}}$ units