Question

33. If l1,m1,n1, and l2, m2, n2, are the direction cosines of two vectors and is the angle between them, then the value of cos is 1) l1 l2 + m1m2, +n1n2 2) l1m1+m1n1 + n1l1 3) l2 M₂ + m₂n2 + n2 l2 4) m1l2+l2 M₂ + n1m2​

Answer 1

Let l, m, n be the direction cosines of the line perpendicular to each one of the given lines.

Then,

Solving and by cross-multiplicatin, we get :

or

,

where is the angle between the given lines.

But, and therefore,

and

Hence, the direction cosines of the required line are

x