a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize L. Find the point Q...
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)
Homework Answers
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a) Let L be the line through (2,-1,1) and (3,2,2). Parameterize L. Find the point Q...
72. Points and lines. Let L be the line passing through the points A (1,1,2) and...
72. Points and lines. Let L be the line passing through the points A (1,1,2) and B=(3,5,6). (a) Use a vector projection to find the closest point P on L to the point C = (2,1,1). (b) Find the distance between P and C.
Let L be the line passing through the point P=(-2,-2, -2) with direction vector d=[3,1, 0]T
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 L be the line passing through the point P(-4, -1,5) with direction vector d=[-3, 3,...
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)
Let L be the line passing through the point P(1,5, -2) with direction vector d=[0,-1, 0]T,...
Let L be the line passing through the point P(1,5, -2) with direction vector d=[0,-1, 0]T, and let T be the plane defined by x–5y+z = 22. Find the point Q where L and T intersect. Q=(0,0,0)
(a) Find symmetric equations for the line that passes through the point (2, -2, 8) and...
(a) Find symmetric equations for the line that passes through the point (2, -2, 8) and is parallel to the vector (-1, 3,-4). -(x + 2) = 3(y-2) = -4(2 + 8). Ox+2-472.28 2-8 -4 -(x - 2) = 3(y + 2) = -4(2-8). *+2.1;2-28 (b) Find the points in which the required line in part (a) intersects the coordinate planes. point of intersection with xy-plane point of intersection with yz-plane point of intersection with xz plane
Question 1 (10 points] Let L be the line passing through the point P=(4, -2,5) with...
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 thr points Q1=(-4,-5,-2) and Q2=(0,-7,2). Find a value of...
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
(1) Equation of a Plane Let P(1,1,-1), Q(1,2,0), R(-2,2,2). (la) Compute PQxPR. (1b) Find the equation...
(1) Equation of a Plane Let P(1,1,-1), Q(1,2,0), R(-2,2,2). (la) Compute PQxPR. (1b) Find the equation of the plane through P, Q and R in the form ax+by+cz=d. (10) What is the angle formed by this plane and the xy-plane?
1. (10) Let l be the line in 3-space that passes through the points A=(5,2, -1)...
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 L be the line with parametric equations x=-5 y=-6- z=9-t Find the vector equation for...
Let L be the line with parametric equations x=-5 y=-6- z=9-t Find the vector equation for a line that passes through the point P=(-3, 10, 10) and intersects L at a point that is distance 5 from the point Q=(-5, -6, 9). Note that there are two possible correct answers. Use the square root symbol 'V' where needed to give an exact value for your answer. 8 N
72. Points and lines. Let L be the line passing through the points A (1,1,2) and B=(3,5,6). (a) Use a vector projection to find the closest point P on L to the point C = (2,1,1). (b) Find the distance between P and C.
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 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)
Let L be the line passing through the point P(1,5, -2) with direction vector d=[0,-1, 0]T, and let T be the plane defined by x–5y+z = 22. Find the point Q where L and T intersect. Q=(0,0,0)
(a) Find symmetric equations for the line that passes through the point (2, -2, 8) and is parallel to the vector (-1, 3,-4). -(x + 2) = 3(y-2) = -4(2 + 8). Ox+2-472.28 2-8 -4 -(x - 2) = 3(y + 2) = -4(2-8). *+2.1;2-28 (b) Find the points in which the required line in part (a) intersects the coordinate planes. point of intersection with xy-plane point of intersection with yz-plane point of intersection with xz plane
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 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
(1) Equation of a Plane Let P(1,1,-1), Q(1,2,0), R(-2,2,2). (la) Compute PQxPR. (1b) Find the equation of the plane through P, Q and R in the form ax+by+cz=d. (10) What is the angle formed by this plane and the xy-plane?
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 L be the line with parametric equations x=-5 y=-6- z=9-t Find the vector equation for a line that passes through the point P=(-3, 10, 10) and intersects L at a point that is distance 5 from the point Q=(-5, -6, 9). Note that there are two possible correct answers. Use the square root symbol 'V' where needed to give an exact value for your answer. 8 N
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