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प्रश्न
Find the component form of `bar"a"` if it lies in YZ-plane makes 60° with positive Y-axis and `|bar"a"| = 4`.
उत्तर
Let α, β, γ be the direction angles of `bar"a"`
Since `bar"a"` lies in YZ-plane, , it is perpendicular to X-axis
∴ α = 90°
It is given that β = 60°
∵ cos2α + cos2β + cos2γ = 1
∴ cos290° + cos260° + cos2γ = 1
∴ 0 + `(1/2)^2` + cos2γ = 1
∴ cos2γ = `1 - 1/4 = 3/4`
∴ cos2γ = `+- sqrt3/2`
Unit vector along `bar"a"` is given by
`hat"a" = ("cos" alpha)hat"i" + ("cos"beta)hat"j" + ("cos"gamma)hat"k"`
`= 0.hat"i" + 1/2hat"j" + sqrt3/2hat"k"`
`= 1/2hat"j" +- sqrt3/2hat"k"`
∴ `bar"a" = |bar"a"|hat"a" = 4(1/2hat"j" +- sqrt3/2hat"k")` .....[∵ `|bar"a"| = 4`]
∴ `bar"a" = 2hat"j" +- 2sqrt3hat"k"`
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