{(5, –3,3), (5,11,5)} or {(–3,5,–1), (8,3,9)}

Sol. Let (5,3,–3) is A, (0,–1,–1) is B, (0,5,11) is C and (5,9,9) is D.

New ABCD is rectangle and diagonal BD has direction cosines as .

It means the vertices whose position is changed are vertices A and C

Let foot of A on BD is F ( λ , –1 + 2 λ , –1+ 2 λ )

Because AE perpendicular to BD, hence 1( λ –5) + 2(2 λ – 4) + 2(2 λ + 2) = 0

⇒ λ = 1

⇒ F is (1,1,1)

Let mid point of BD is E =

Normal vector to plane ABCD is

=

= –60 + 60 – 30

or

Now distance between A and F is 6

⇒ New position of A is or

⇒ New A is either (–3,5,–1) or (5,–3,3)

If new A is (–3,5,–1) then new C is (8,3,9)and if new A is (5,–3,3) then new C is (5,11,5)

(calculate new C by applying mid point formula)

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