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  4. Find the orthocentre of the triangle formed by the vertices A (5,-2), B (-1,2) and C (1,4)

Q. Find the orthocentre of the triangle formed by the vertices $A (5,-2), B (-1,2)$ and $C (1,4)$

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Solution:

given $\Rightarrow \cos ^{-1} x=\cos ^{-1} y=\cos ^{-1} z=\pi$
$\Rightarrow x=y=z=\cos \pi=-1$
$\therefore x+y+z=-1-1-1=-3 \& \frac{1}{x+y+z}=\frac{1}{-3}=-\frac{1}{3}$
$\therefore x+y+z+\frac{1}{x+y+z}=-\frac{3}{1}-\frac{1}{3}=\frac{-10}{3}$

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