Question

Let \[ A=(2,0,3),\qquad B=(0,1,4),\qquad C=(5,6,0) \] be three points. If \(L_1\) and \(L_2\) are the lines bisecting the angles between \(AB\) and \(AC\), then the direction ratios of the line perpendicular to both \(L_1\) and \(L_2\) are

• A. \((3,1,2)\)
• B. \((1,5,2)\)
• C. \((3,1,5)\)
• D. \((1,3,5)\)

Hint:

If two lines have direction vectors \[ \vec d_1,\qquad \vec d_2, \] then a line perpendicular to both has direction vector \[ \boxed{\vec d_1\times\vec d_2.} \]

Answer 1

The Correct Option is C