In a triangle ABC, if $$|\overrightarrow {BC} | = 8,|\overrightarrow {CA} | = 7,|\overrightarrow {AB} | = 10$$, then the projection of the vector $$\overrightarrow {AB} $$ on $$\overrightarrow {AC} $$ is equal to :

Define a relation R over a class of n $$\times$$ n real matrices A and B as

"ARB iff there exists a non-singular matrix P such that PAP^$$-$$1 = B".

Then which of the following is true?

Let the centroid of an equilateral triangle ABC be at the origin. Let one of the sides of the equilateral triangle be along the straight line x + y = 3. If R and r be the radius of circumcircle and incircle respectively of $$\Delta$$ABC, then (R + r) is equal to :

Consider a hyperbola H : x² $$-$$ 2y² = 4. Let the tangent at a
point P(4, $${\sqrt 6 }$$) meet the x-axis at Q and latus rectum at R(x₁, y₁), x₁ > 0. If F is a focus of H which is nearer to the point P, then the area of $$\Delta$$QFR is equal to :