# 20.  Find the vector equation of the line passing through the point (1, 2, – 4) and perpendicular to the two lines:               and

Given

Two straight lines in 3D whose direction cosines (3,-16,7) and (3,8,-5)

Now the two vectors which are parallel to the two lines are

and

As we know, a vector perpendicular to both  vectors  and  is , so

A vector parallel to this vector is

Now as we know the vector equation of the line which passes through point p and parallel to vector d is

Here in our question, give point p = (1,2,-4) which means position vector of this point is

So, the required line is

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