Question

The projections of a vector on the three coordinate axis are 6,-3,2 respectively.The direction cosines of the vector are

Answer 1

Answer:

If cosα,cosβ,cosγ are the direction cosines then rcosα=6,rcosβ=−3,rcosγ=2

Squaring ,r

2

cos

2

α=36,r

2

cos

2

β=9,r

2

cos

2

γ=4

⇒r

2

cos

2

α+r

2

cos

2

β+r

2

cos

2

γ=(36+9+4)=49

⇒r

2

(cos

2

α+cos

2

β+cos

2

γ)=49

⇒r

2

=49,r=7

∴ the direction cosines are

7

6

,

7

−3

,

7

2

Step-by-step explanation:

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