Question

Find the angle between the vectors whose direction cosines are proportional to $2,3,-6$ and $3,-4,5$.

Answer 1

Let, $\theta$ is the angle between two lines whose direction cosines are,

$l_1=2,m_1=3,n_1=-6;$

$l_2=3,m_{{}_2}=-4,n_2=5;$

We know that,

$\cos \theta =l_1{l}_2+m_1{m}_2+n_1{n}_2$

$=2\times 3+3\times (-4)-6\times 5$

_$=6-12-30$

_$=-36$

_Therefore,

_{$\cos \theta =-36$}

_{$\theta ={\cos }^{-1}(-36)$}

Not possible because $-1\le \cos \theta \le 1$

Hence question is wrong.