If $x = 2, y = - 1, z = 4$ ; find the value of the following expression $x^{2} + y^{2} + z^{2} - x y - y z - z x$ .

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Solution

For $x = 2, y = - 1, z = 4$
$x^{2} + y^{2} + z^{2} - x y - y z - z x = (2)^{2} + (- 1)^{2} + 4^{2} - (2) (- 1) - (- 1) (4) - 2 (4) = 4 + 1 + 16 + 2 + 4 - 8 = 19$

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