What is direction cosine and ration math is fun?
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Yea offcourse it's fun
we have find direction cosines (D.C)and ratio(D.R) of vector PQ with P(x₁,y₁,z₁) Q(x₂,y₂,z₂)
magnitude of vector PQ=√[(x₂- x₁)²+(y₂- y₁)²+(z₂- z₁)² ]=r
let vector make angle α with x-axis,β with y-axis ,γ with z-axis
D.C. are cosα,cosβ,cosγ
D.R. simply are (x₂ -x₁), (y₂- y₁), (z₂ -z₁)
D.R from D. C and r
As, cosα=(x₂-x₁)/r, cosβ=(y₂- y₁)/r, cosγ=(z₂- z₁)/r
(x₂ -x₁)=r *cosα, (y₂-y₁)=r *cosβ (z₂-z₁)=r* cosγ
At last , D.C are unique means always fixed for a partucular vector
but D.C are not
we have find direction cosines (D.C)and ratio(D.R) of vector PQ with P(x₁,y₁,z₁) Q(x₂,y₂,z₂)
magnitude of vector PQ=√[(x₂- x₁)²+(y₂- y₁)²+(z₂- z₁)² ]=r
let vector make angle α with x-axis,β with y-axis ,γ with z-axis
D.C. are cosα,cosβ,cosγ
D.R. simply are (x₂ -x₁), (y₂- y₁), (z₂ -z₁)
D.R from D. C and r
As, cosα=(x₂-x₁)/r, cosβ=(y₂- y₁)/r, cosγ=(z₂- z₁)/r
(x₂ -x₁)=r *cosα, (y₂-y₁)=r *cosβ (z₂-z₁)=r* cosγ
At last , D.C are unique means always fixed for a partucular vector
but D.C are not
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Answer:
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