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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
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.
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...
Question 7 (10 points] Let Ly be the line passing through the points Q1-(3,-1,-4) and Q2=(5,-3,-2) and let La be the line passing through the point P4-(12,-4, 3) with direction vector a-(-6, -6, -21". Determine whether Ly and L2 intersect. If so, find the point of intersection Q. The lines intersect at the following point Q: Q=(0,0,0)
Let L be the line passing through the point P(-4, -1,5) with direction vector d=[-3, 3, 2]T, and let T be the plane defined by 3x+2y-5z =-9. Find the point Q where L and T intersect. Q=(0, 0, 0)