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The direction cosines x,y,z of a line are connected by a relation ${(x + y)}^{2} - a^{2} = 2 x y - z^{2}$ Then $\sqrt{a^{2} + 5 a + 2019} =$

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Correct option is D

If x,y,zare direction cosines of a line then x2+y2+z2=1Consider the equation (x+y)2−a2=2xy−z2Expand and then simplify x2+y2+2xy−a2=2xy−z2⇒x2+y2+z2=a2⇒a2=1It implies that a=1Hence the value of a2+5a+2019 is 1+5+2019=2025=45

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The direction cosines x,y,z of a line are connected by a relation (x+y)2−a2=2xy−z2 Thena2+5a+2019=

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The direction cosines x,y,z of a line are connected by a relation ${(x + y)}^{2} - a^{2} = 2 x y - z^{2}$ Then $\sqrt{a^{2} + 5 a + 2019} =$