Question

If two lines have direction cosines

$l_1,m_1,n_1$ and $l_2,m_2,n_2$

then the condition for these lines being perpendicular to each other would be -

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is A

Two lines being perpendicular to each other means the angle between these lines is ${90}^{\circ }$.
Angle between two lines is given as-
$i.e.\cos \left(\theta \right)=(l_1.l_2+m_1.m_2+n_1.n_2)$
Where $l_1,m_1,n_1$ are the direction cosines of one line and $l_2,m_2,n_2$ are the direction cosines of another.
If we put $\theta$ =${90}^{\circ }$ , we’ll get the condition for perpendicularity.
So, $cos\left({90}^{\circ }\right)=(l_1.l_2+m_1.m_2+n_1.n_2)$
Or,

$l_1.l_2+m_1.m_2+n_1.n_2=0$ $[\because \cos {90}^0=0]$

Hence, the correct option is (A).