Question

Find direction angles and direction cosines of the given vector.

Answer 1

Dear Student: Given:  v= 5i+12j+84k

Generally  direction cosine of a vector v = ai+bj+ck are

$cosA=\frac{a}{\sqrt{(a^{2}+b^{2}+c^{2} )  } }$

$cosB=\frac{b}{\sqrt{(a^{2}+b^{2}+c^{2} )  } }$

$cosC=\frac{c}{\sqrt{(a^{2}+b^{2}+c^{2} )  } }$

$cosA=\frac{5}{\sqrt{(5^{2}+12^{2}+84^{2} )  } }$

$cosB=\frac{12}{\sqrt{(5^{2}+12^{2}+84^{2} )  } }$  

$cosC=\frac{84}{\sqrt{(5^{2}+12^{2}+84^{2} )  } }$

$cosA=\frac{5}{85}$

$cosB=\frac{12}{85}$

$cosC=\frac{84}{85}$

A,B and C are direction angles.

$A=cos^{-1}(\frac{1}{17})$

$B=cos^{-1}(\frac{12}{85})$

$C=cos^{-1}(\frac{84}{85})$

Hope it helps Thanks With Regards

 

Answer 2

In the attachments I have answered this problem.         Concept:         Angles made by a line or a vector with the  co ordinate axes are called direction angles.         Cosine value of these angles are called direction coseines of the vector.           See the attachment for detailed solution.