If the two directional cosines of a vector are 12 &13 then the value of third directional cosine is

cos2α+cos2β+cos2γ=1(12)2+(13)2+cos2γ=1⇒ cos2γ=1−12−13=16 ⇒ cosγ=16

If the two directional cosines of a vector are 12 &13 then the value of third directional cosine is

cos2α+cos2β+cos2γ=1(12)2+(13)2+cos2γ=1⇒ cos2γ=1−12−13=16 ⇒ cosγ=16

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If the two directional cosines of a vector are $\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}}$ then the value of third directional cosine is

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$\frac{1}{\sqrt{7}}$

$\frac{1}{\sqrt{10}}$

$\frac{1}{\sqrt{6}}$

$\frac{1}{\sqrt{5}}$

answer is C.

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$\cos^{2} α + \cos^{2} β + \cos^{2} γ = 1$

${(\frac{1}{\sqrt{2}})}^{2} + {(\frac{1}{\sqrt{3}})}^{2} + \cos^{2} γ = 1$

$\Rightarrow \cos^{2} γ = 1 - \frac{1}{2} - \frac{1}{3} = \frac{1}{6} \Rightarrow \cos γ = \frac{1}{\sqrt{6}}$

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If the two directional cosines of a vector are 12 &13 then the value of third directional cosine is

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If the two directional cosines of a vector are $\frac{1}{\sqrt{2}} & \frac{1}{\sqrt{3}}$ then the value of third directional cosine is