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Question 4 Consider the lines L, D=1+2, y = 2 – 3t, z = 2+t and L2 X = 3 - 4s, y=1+ 48, z = -3 + 48. We will use these lines for the questions 4 and 5. Are these lines parallel? Explain your answer below. B IV A - A - Ix E - C o o x G You HTML 11 x Ⓡ 5E T To 12pt Pan Question 5 9 pts Determine where these lines...
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.
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...
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...
Determine whether the given lines intersect. If so, find the point of intersection. (If not, enter NOT.) x = 6 + t, y = 3 + t, z = -1 + 2t x = 8 + 2s, y = 9+ 4s, z = -3 + S (x, y, z) = eBook
Math 32-_ Multivariable Calculus HW 3 (1) Consider the two straight lines L1 : (2-t, 3 + 2t,-t) and L2 : <t,-2 + t, 7-20 a) Verify that L1 and L2 intersect, and find their point of intersection. (b) Find the equation of the plane containing L1 and L2 (2) Consider the set of all points (a, y, z) satisfying the equation 2-y2+220. Find their intersection 0 and 2-0. Use that information to sketch a with the planes y =-3,-2,-1,0,...
1) Show that two lines are skew x+1 y+2 z+3 4:x=y=z and L: +7=5 2) Find the general equation of the plane containing the point P (1,2,3 ) and L, . 3) Find the point Q-the point of intersection the plane found in 2) and the line L. 4) Find the distance from the point (1,-1,2) to the line Lą.
(I point) Let F=21+(z + y) j + (z _ y + z) k. (1+4t). y = 4 + 2t, z = _ (1+t). Let the line l be x =- (a) Find a point P-(zo, 30, zo) where F is parallel to 1. Find a point Q (which F and I are perpendicular. Q= and l are perpendicular Give an equation for the set of all points at which F and l are perpendicular. equation: (I point) Let F=21+(z...
Please provide clear handwritings for answers and specific step by step explanations of questions 3 and 4. Thank you. 3. Are the plane 6z 3y - 4z-12 and line L 2, y 32t, z2-2t parallel? If so, find the distance between them. If they are not parallel, but are intersecting (at a single point), find the point of intersection. If they are none of the above, draw a cat. 4. The line r(t) = 〈1, 1,1〉 +t(1,3,-1) and the plane...
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