If three mutually perpendicular lines have direction cosines `(l_1,m_1,n_1),(l_2,m_2,n_2) and (L_3 ,m_3, n_3)`, then the line having direction cosines `l_1+l_2+l_3,m_1+ m_2+m_3, and n_1 + n_2 + n_3`, make an angle of

Explanation

`vec{a}=l_{1} hat{i}+m_{1} hat{j}+n_{1} widehat{k} `

`
vec{b}=l_{2} hat{i}+m_{2} hat{j}+n_{2} widehat{k} `

`
vec{c}=l_{3} hat{i}+m_{3} hat{j}+n_{3} widehat{k}`



the direction vector associated with directions cosines ` I_{1}+I_{2}+I_{3}, m_{1}+m_{2}+m_{3}, n_{1}+n_{2}+n_{3}`

`

vec{p}=(1_{1}+l_{2}+l_{3}) hat{i}+(m_{1}+m_{2}+m_{3}) hat{i}+(n_{1}+n_{2}+n_{3}) widehat{k}`



...