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Chapter 10: Q .50. (page 812)

$\cos 尾 = \frac{1}{4}, \cos 纬 = \frac{1}{3} .$

Short Answer

Expert verified

$The value of the third direction cosine is 卤 \frac{\sqrt{119}}{12}$

Step by step solution

01

Step 1:Given information

$\cos 尾 = \frac{1}{4}, \cos 纬 = \frac{1}{3} .$

02

Step 2:Simplification

$Consider the direction cosines \cos 尾 = \frac{1}{4}, \cos 纬 = \frac{1}{3} .$

$The objective is to find the third direction cosine using the result Consider the direction cosines$

$\cos^{2} 伪 + \cos^{2} 尾 + \cos^{2} 纬 = 1$

$Also, \cos^{2} 伪 + \cos^{2} 尾 + \cos^{2} 纬 = 1$

$Now, since \cos 尾 = \frac{1}{4}, \cos 纬 = \frac{1}{3} .$

$Substitute the values in (1)$

$\cos^{2} 伪 + {(\frac{1}{4})}^{2} + {(\frac{1}{3})}^{2} = 1$

$\cos^{2} 伪 + \frac{1}{16} + \frac{1}{9} = 1$

$\cos^{2} 伪 + \frac{9 + 16}{144} = 1$

$\cos^{2} 伪 + \frac{25}{144} = 1$

$\cos^{2} 伪 = 1 - \frac{25}{144}$

$\cos 伪 = 卤 \frac{\sqrt{119}}{12}$

$Hence, the value of the third direction cosine is 卤 \frac{\sqrt{119}}{12}$

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