Question

determine whether the lines intersect and if so find the point of intersection and the cosine of the angle of intersection x=4t+2 y=3 z=-t+1.

Answer 1

Answer:

As the lines are not intersecting nor parallel, they must be skew.

Step-by-step explanation:

Question is incomplete, we consider the nearest match available online.

Parametric equations of two lines are:

L₁ : x=4t+2 , y = 3 , z =-t+1

L₂: x=2s+2 , y= 2s+5 , z = s+1

If lines are parallel then parametric coordinates must be equal scalar multiple of each other which s not true here.

$4t+2=2s+2 ---(1)\\ \\3=2s+5---(2) \\\\-t+1=s+1---(3)$

If lines are intersecting then parametric coordinates must be equal for some value of t and s.

$From (3)\\-t=s\\From (2)\\\\s=\frac{3-5}{2}\\\\s=-1\\\implies t=1\\\\To\,\,check\,\, the \,\,values \,\,of \,\,s\,\, and \,\,t \,\,for\,\,intersection\,\,put \,\,them\,\, in\,\, (1)\\\\4(1)+2= 2(-1)+2\\ 6\ne0$

Hence the lines are not intersecting nor parallel, they must be skew.