If a variable line in two adjacent positions has direction cosines l, m,n and l+∂l, m+∂m, n+∂n, show that the small angle ∂theta between the two postions is given by (∂theta) 2 = (∂l) 2 + (∂m) 2 +(∂n) 2

Question

If a variable line in two adjacent positions has direction cosines l, m,n and l+∂l, m+∂m, n+∂n, show that the small angle ∂theta between the two postions is given by (∂theta) 2 = (∂l) 2 + (∂m) 2 +(∂n) 2

Sourabh Singh · Answer

Use the formula of angle between the lines and after that Use approximation to eliminate the trigonometric functionality. You will get the answer. Best of Luck

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If a variable line in two adjacent positions has direction cosines l, m,n and l+∂l, m+∂m, n+∂n, show that the small angle ∂theta between the two postions is given by (∂theta) 2 = (∂l) 2 + (∂m) 2 +(∂n) 2

If a variable line in two adjacent positions has direction cosines l, m,n and l+∂l, m+∂m, n+∂n, show that the small angle ∂theta between the two postions is given by
(∂theta)²= (∂l)² + (∂m)²+(∂n)²

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If a variable line in two adjacent positions has direction cosines l, m,n and l+∂l, m+∂m, n+∂n, show that the small angle ∂theta between the two postions is given by (∂theta) 2 = (∂l) 2 + (∂m) 2 +(∂n) 2

If a variable line in two adjacent positions has direction cosines l, m,n and l+∂l, m+∂m, n+∂n, show that the small angle ∂theta between the two postions is given by(∂theta)2= (∂l)2 + (∂m)2+(∂n)2

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If a variable line in two adjacent positions has direction cosines l, m,n and l+∂l, m+∂m, n+∂n, show that the small angle ∂theta between the two postions is given by
(∂theta)²= (∂l)² + (∂m)²+(∂n)²