If `alpha,beta,a n dgamma` are the an gles which a directed line makes with the positive directions of the co-ordinates axes, then find the value of `

Question

If `alpha,beta,a n dgamma` are the an gles which a directed line makes with the positive directions of the co-ordinates axes, then find the value of `

If `alpha,beta,a n dgamma` are the an gles which a directed line makes with the positive directions of the co-ordinates axes, then find the value of `sin^2alpha+sin^2beta+sin^2gammadot`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

The direction cosines of the line are `l=cosalpha, m=cosbeta and n=cosgamma.`
`because" "l^(2)+m^(2)+n^(2)=1, cos^(2)alpha+cos^(2)beta+cos^(2)gamma=1`
`therefore" "1-sin^(2)alpha+1-sin^(2)beta+1-sin^(2)gamma=1`
`or" "sin^(2)alpha+sin^(2)beta+sin^(2)gamma=2`

5 views Answered 2023-02-05 15:29