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72. Points and lines. Let L be the line passing through the points A (1,1,2) and...
a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize L. Find the point Q where L intersects the xy-plane. b) Find the angle that the line through (0,-1,1) and (√3,1,4) makes with a normal vector to the xy-plane. c) Find the distance from the point (3,1,-2) to the plane x-2y+z=4. d) Find a Cartesian equation for the plane containing (1,1,2), (2,1,1) and (1,2,1)
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.
Let L1 be the line passing through thr points Q1=(-4,-5,-2)
and Q2=(0,-7,2). Find a value of k so the line L2 passing through
the point P1=(7,-9,k) with direction vector d=[-1,-1,0]^t
intersects with L1
K=??
Question 2 [10 points) Let Ly be the line passing through the points Or.-5. 2) and Q-0-72) Find a value of k so the line passing through the point Ps-P;(7.-9. k) with direction vector i/-/-1,-1.0" intersects with L ko
Find the equation of the line passing through the point (1,1,1) which is perpendicular to the plane containing the points (1,0,0), (2,1,1) and (1,1,2).
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)...
Question 1 (10 points] Let L be the line passing through the point P=(4, -2,5) with direction vector d=[5, 2, 2]', and let T be the plane defined by –2x-3y=z=-5. Find the point Q where L and T intersect. Q=(0,0,0)
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.
(a) find the vector equation (b) the cartesian equation of the straight line passing through the points A(2,-1,3) and parallel to line through the points B(3,2,-1) and C(-1,1,2). verify that the point (-2,-2,6) is on the required line
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...