4) Do the lines: L: x = 2t + 3, y = 3t – 2, z = 4t - 1 and L2 : x = 8 +6, y = 2s + 2, z = 2s + 5 intersect? If not provide a reason, if yes find the intersection point.
Question 3 (1 point) Consider the lines: L1: x=-6t, y=1+9t, z=-3t L2: x=1+2s, y=4-3s, z=s Choose their intersection point from below (0,0,1) none (1,2,1) (0,1,0)
3. (14 points) Given the lines: 21:2(t) = -3t – 1, y(t) = 2t +4, z(t) =t+4 12: x(u) = 5 - 3u, y(u) = u +1, (u) = u +2 1. Determine whether li and ly are parallel, skew or intersect. If the lines intersect, find the point of intersection of li and 12. 2. If the lines intersect or are parallel, give an equation for the plane which contains both lines. If the lines are skew, find a...
Calculate the distance between the lines L1:x=1+3t,y=−5+3t,z=−3+1t L1 and L2:x=8+4s,y=−13+5s,z=0+4s
(1 point) Determine whether the lines li: x = 8 + 2s, y = 19 + 5s, z = 3 + 2s, SER and l2: x = -4 + 3t, y = -10 + 7t, z = -13 + 5t, tER intersect, are skew, or are parallel. If they intersect, determine the point of intersection; if not leave the remaining answer blanks empty. Do/are the lines: ? Point of intersection:
3. Determine the intersection of the two lines, if any: 2 y+1; z 1. 3 L2: =5-t. y = t, 2 = 1-+3t, t E R L and evaluate the distance between R(1, 1. -1) and Li 3. Determine the intersection of the two lines, if any: 2 y+1; z 1. 3 L2: =5-t. y = t, 2 = 1-+3t, t E R L and evaluate the distance between R(1, 1. -1) and Li
56. Let Li and L2 be the lines whose parametric equations are L]: x = 41, y = 1 -21, z = 2 + 21 L2: x = 1+1, y = 1-1, Z=-1+ 41 (a) Show that Li and L2 intersect at the point (2,0, 3). (b) Find, to the nearest degree, the acute angle between L and L2 at their intersection. c) Find parametric equations for the line that is perpen- dicular to L, and L2 and passes through...
Find the plane determined by the intersecting lines. L1 x= -1 +41 y=2+t z= 1 - 4 L2 x = 1 - 4s y= 1 + 25 z=2-2s The equation of the plane is (Type an equation.)
(a) Let L and L' be two lines in R3. 1:*2 =12-21 Lt -1 5 -2 -1 2-5 -4. Determine if the lines intersect at a point. If the , write down the three coordinates of the intersection point in the three boxes below. If they do not, enter the three letters D, N, E, one in each box below (for Does NotExist) (b) An insect is flying along a path r(x,y,z) = (x(t), y(t), z(t)) in a room where...
Question 14 5 pts Consider the parametrically defined curve a. x = 6sin(3t), y=t, z = 6cos(3t); (0,71,- 6) Find the equation of the osculating plane of the curve at the given point 4x + 18y = 18 b. X + 18y = 1871 4x - y = - 1871 d. X - 18y = - 1871 x + 18y = - 1871 C. e. a Ob С Od e