Find the acute angle which the line with direction cosines 1-3- 1-6- n makes with positive direction of z-axis-

As 1^2 +m^2 +n^2 =1 ∴ (1/√(3) )^2 + (1/√(6) )^2 +n^2 =1 ⇒ n =1/√(2) = cos γ∴γ =π/4. Here γ is the acute angle made by the line with positive direction of z axi ...

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Standard XII

Mathematics

Slope Intercept Form of a Line

Find the acut...

Question

Find the acute angle which the line with direction cosines $\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{6}}$ , n makes with positive direction of z -axis.

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Solution

As $1^{2} + m^{2} + n^{2} = 1 ∴ {(\frac{1}{\sqrt{3}})}^{2} + {(\frac{1}{\sqrt{6}})}^{2} + n^{2} = 1 \Rightarrow n = \frac{1}{\sqrt{2}} = c o s γ ∴ γ = \frac{π}{4} .$
Here $γ$ is the acute angle made by the line with positive direction of z-axis.

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Find the acute angle which the line with direction cosines 1√3,1√6, n makes with positive direction of z -axis.

As 12+m2+n2=1∴(1√3)2+(1√6)2+n2=1⇒n=1√2=cosγ∴γ=π4. Here γ is the acute angle made by the line with positive direction of z-axis.

Find the acute angle which the line with direction cosines $\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{6}}$ , n makes with positive direction of z -axis.

As $1^{2} + m^{2} + n^{2} = 1 ∴ {(\frac{1}{\sqrt{3}})}^{2} + {(\frac{1}{\sqrt{6}})}^{2} + n^{2} = 1 \Rightarrow n = \frac{1}{\sqrt{2}} = c o s γ ∴ γ = \frac{π}{4} .$
Here $γ$ is the acute angle made by the line with positive direction of z-axis.