Let L be the line with parametric equations x=-5 y=-6- z=9-t Find the vector equation for...
Let L be the line passing through the point P=(4, 5, −2) with direction vector →d=[2, 2, 0]T. Find the shortest distance d from the point P0=(1, 1, −2) to L, and the point Q on L that is closest to P0. Use the square root symbol '√' where needed to give an exact value for your answer.
Let L be the line passing through the point P=(-2,-2, -2) with direction vector d=[3,1, 0]T. Find the shortest distance d from the point P0=(-2,-3, -2) to L, and the point Q on L that is closest to Po. Use the square root symbol '√' where needed to give an exact value for your answer.
Find the point at which the line with the parametric equations x-1-1, y=1+1, z intersects the plane with the equation X-y +3.2-4.
2. Find a vector equation and parametric equations for the line segment that joins P to Q: P(-2, 4,0), Q(6,-1,2)
Let L1 be the line passing through the point P1(4, 3, 1) with direction vector d=[-1, 1, -3]T, and let L2 be the line passing through the point P2(-1, 2, -5) with the same direction vector. Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that d(Q1,Q2) = d. Use the square root symbol '√' where needed to give an exact value for your answer. d = _______ Q1...
Let L1 be the line passing through the point P1(5,3, 2) with direction vector d=[2, 1, -2]T, and let L2 be the line passing through the point P2(-3,1,-4) with the same direction vector. Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that d(Q1,Q2)=d. Use the square root symbol '√' where needed to give an exact value for your answer.
1. (10) Let l be the line in 3-space that passes through the points A=(5,2, -1) and B = (6,0,–7). (a) Find a set of parametric equations for l. (b) Find the unique point P at which l intersects the plane with equation -3.21 + 722 - 2.23 = 11. (c) Let P be the point found in part (b), and let Q = (k, 7, 10) for an unspecified real number k. Determine the value of k for which...
Let L1 be the line passing through the point P 2, 2,-1) with direction vector a=[-1, 1,-2]T, and let L2 be the line passing through the point P2-(-5, -5,-3) with the same direction vector. Find the shortest distance d between these two lines, and find a point Q1 on L1 and a point Q2 on L2 so that dQ1Q2) d. Use the square root symbol' where needed to give an exact value for your answer. d 0 Q1-(0, 0, 0)...
(1 point) Give a vector parametric equation for the line that passes through the point (1, -5, -1), parallel to the line parametrized by (-3 – t, 1+ 4t, 4+t): L(t) =
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...