Find both the vector equation and the para metric equations of the line through [DJ], E} in the direction of the vector v = { E, 4.0}, where t= [I corresponds to the given point. The vector equation is {x312} = iii:ii:i'i:i} + I: Find both the vector equation and the parametric equations of the line through [ 4,2,5} and [2,1,U], where t= 1] corresponds to the rst given point. I The 1rector equation is {3:31} = HELD + IE \fFind parametric equations for the line eegment joining the first paint to the second point. {11.110} and {3,5,1} The parametric equaens are x: D yr = D, z: D for |:l Determine whether the following pair of lines is parallel, intersects at a single point, or is skew. If the lines are parallel, determine whether they are the same line [and thus intersect at all points]. lfthe lines intersect at a single point, determine the point of intersection. x=4.'f=5t.2=1+tand)r= _1_55:3l=1+23.2='l-5 Select the correct choice loelow and, if necessary, ll in any answer boxes to complete your choice. 0 A- The lines intersect at the single point [ENDED . [Simplify your answers.) Q B. The lines are parallel. Q C. The lines are skew. O D. The lines intersect at all points on the line r{t}. Consider the following lines. riti= {3t+1.3t2.3t+3}, for -ocr<:t r oos a. determine whether the lines intersect a common point and if so nd coordinates of that point. b. descri he paths two particles do collide assume te l s e measure time in seconds. select correct choice below it necessary. fill answer box to complete your answer. a- at el. type an ordered triple. not intersect. find equation plane is parallel vecto rs passing through r.: e. using yr as variables. exists iwhich following line y="E;" for m e:r necessary ll which d. angle between planes smallest t normal veetors where diredions nonnal vectors are chosen h planes2x d round until nal then nearest degree needed.>