The direction cosines of a variable I in 2 adj. positions are LMN , L+(DELTA)N , N+(DELTA)M ,AND M +(DELTA)L. Show that 4 small angle delta theta, b/w 2 positions is given by :[delta theta]^2 = {(DELTA)L}^2+[(DELTA)M]^2+[(DELTA)N]^2

Dear Jasmine,

Using the property,

If v is a vector

where  is a basis. Then the direction cosines are

Note that

α² + β² + γ² = 1

And approximation ,

we can get the required answer.

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