the straight line L1 is described by the equation 3x + 4Y + 5 = 0....
the straight line L1 is described by the equation 3x + 4Y + 5 =
0. the straight line L2 is perpendicular to L4. lines L1 and L2
intersect at the point (1, -2)
Give an example of another point than (1, -2) located on L2
Homework Answers
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the straight line L1 is described by the equation 3x + 4Y + 5 =
0....
y^2-3x-4y-1=0 3. Find the equation of the tangent line and the equation of the perpendicular line...
y^2-3x-4y-1=0
3. Find the equation of the tangent line and the equation of the perpendicular line to the curve y? - 3x - 4y - 1 = 0 at (-2, 1) at the given point. 2 marks.
(1) (a) Find the equation of the line, Li, which passes through the points A :...
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
(1 point) The planes 3x + 4y + z = 2 and 3x – 3y =...
(1 point) The planes 3x + 4y + z = 2 and 3x – 3y = -18 are not parallel, so they must intersect along a line that is common to both of them. The vector parametric equation for this line is L(t) =
Given lines L1 : Ty (1-1)+(21) -2 1 and L2: y 4 8+t2 3 (a) Find...
Given lines L1 : Ty (1-1)+(21) -2 1 and L2: y 4 8+t2 3 (a) Find the point of intersection of lines Lị and L2. (b) Determine the cosine of the angle between lines L, and L2 at the point of intersection. © Find an equation in form ax +by+cz = d for the plane containing lines L, and Lu. (d) Find the intersection, if any, of the line Ly and the plane P : 3x – 4y + 72...
write an equation for the line described. give your answer in slope intercept form. perpendicular to...
write an equation for the line described. give your answer in slope intercept form. perpendicular to 3x+4y=24, through (9,8)
Let L1 be the line passing through the points Q1(−2, −5, −3) and Q2(2, −3, −1)...
Let L1 be the line passing through the points Q1(−2, −5, −3) and Q2(2, −3, −1) and let L2 be the line passing through the point P1(11, 1, 4) with direction vector d=[3, 1, 2]T. Determine whether L1 and L2 intersect. If so, find the point of intersection Q.
through tne po State the equation of the straight line parallel to the line y point...
through tne po State the equation of the straight line parallel to the line y point (-4, 5). 3x+ 7 and passing through the 3. Given the linear equations: 2y 3x - 7 2x 5-3y 2y 3x 8 Write the three equations in the form y=mx +c. Hence state: (a) which pair of straight lines are parallel (b) which pair of straight lines are perpendicular to each other. Prove your answer in each case.
Let L1 be the line passing through the point P 2, 2,-1) with direction vector a=[-1,...
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)...
5. (20 points) Given a line segment L1, defined by the parametric equation to follow, find...
5. (20 points) Given a line segment L1, defined by the parametric equation to follow, find another line segment with length 3 which is perpendicular to L1. Note: more than one solution exists.
A is the point (-1, 5). Let (x, y) be any point on the line y = 3x.
A is the point (-1, 5). Let (x, y) be any point on the line y = 3x. a Write an equation in terms of x for the distance between (x, y) and A(-1,5). b Find the coordinates of the two points, B and C, on the line y = 3x which are a distance of √74 from (-1,5). c Find the equation of the line l1 that is perpendicular to y = 3x and goes through the point (-1,5). d Find the coordinates...
y^2-3x-4y-1=0
3. Find the equation of the tangent line and the equation of the perpendicular line to the curve y? - 3x - 4y - 1 = 0 at (-2, 1) at the given point. 2 marks.
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
(1 point) The planes 3x + 4y + z = 2 and 3x – 3y = -18 are not parallel, so they must intersect along a line that is common to both of them. The vector parametric equation for this line is L(t) =
Given lines L1 : Ty (1-1)+(21) -2 1 and L2: y 4 8+t2 3 (a) Find the point of intersection of lines Lị and L2. (b) Determine the cosine of the angle between lines L, and L2 at the point of intersection. © Find an equation in form ax +by+cz = d for the plane containing lines L, and Lu. (d) Find the intersection, if any, of the line Ly and the plane P : 3x – 4y + 72...
through tne po State the equation of the straight line parallel to the line y point (-4, 5). 3x+ 7 and passing through the 3. Given the linear equations: 2y 3x - 7 2x 5-3y 2y 3x 8 Write the three equations in the form y=mx +c. Hence state: (a) which pair of straight lines are parallel (b) which pair of straight lines are perpendicular to each other. Prove your answer in each case.
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)...
5. (20 points) Given a line segment L1, defined by the parametric equation to follow, find another line segment with length 3 which is perpendicular to L1. Note: more than one solution exists.
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