We know that,If l, m and n are direction cosines of a line, then l2 + m2 + n2 = 1Now, l = cos α; m = cos β; n = cos γSo, cos2α + cos2β + cos2γ = 1⇒14152 + 132 + cos2γ = 1⇒196225 + 19 + cos2γ = 1⇒196+25225 + cos2γ = 1⇒cos2γ = 1 - 221225 = 4225⇒cos γ = ±215

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We know that, If l, m and n are direction cosines of a line, then l^{2} + m^{2} + n^{2} = 1 Now, l = \cos α; m = \cos β; n = \cos γ So, \cos^{2} α + \cos^{2} β + \cos^{2} γ = 1 \Rightarrow {(\frac{14}{15})}^{2} + {(\frac{1}{3})}^{2} + \cos^{2} γ = 1 \Rightarrow \frac{196}{225} + \frac{1}{9} + \cos^{2} γ = 1 \Rightarrow \frac{196 + 25}{225} + \cos^{2} γ = 1 \Rightarrow \cos^{2} γ = 1 - \frac{221}{225} = \frac{4}{225} \Rightarrow \cos γ = \pm (\frac{2}{15})

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