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Engineering Mathematics, Volume I, Second Edition by Babu Ram

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Multiplying (4), (5), and (6) by x, y, and z and adding, we obtain

 

images

 

so,

r2 + λ1 = 0, which gives λ1 = – r2.

 

Hence, from (4), (5), and (6), we have

 

images

 

Putting these values of x, y, and z inn lx + my + nz = 0, we get

 

images

 

Since λ2 ≠ 0, the equation giving the values of r2, the squares of the length of the semi-axes, is

EXAMPLE 5.110

If a, b, and, c are positive and

 

 

show that a stationary value of u is given by

 

 

where μ is ...

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