Problem 4: Find the line equation for the line which passes through (1,3,4) and is perpendicular to the plane 3x – 2y + z = 5. Express your final answer in vector form, parametric form, AND symmetric form.

Q: QUESTION 5 Find a vector equation of the line through point (6.0.2) and parallel to the line with…

A: Given:x=4-3ty=-1+4tz=6+5tPoint 6,0,2

Q: 11. Find parametric equations for the line that contains the points P(2, -4, 7) and Q(0, –3, 5).

A: If Px0 ,y0,z0 and Qx1,y1,z1 are any two points then the parametric equation of the line containing…

Q: Complete the parametric equations for the line where the planes – 3x – 9y – 12z - 11x + 2y – 10z 33…

A:

Q: 1) Find parametric equations for the line which contains A(2,0, 1) and B(-1,1, –1).

A:

Q: Problem 5: Find the equation for the plane which passes through (1,5,7) that contains the line given…

A: To Determine: Find the equation for the plane which passes through (1,5,7) that contains the line…

Q: Question 3 Find the parametric representation of the straight line that passes through the points…

A: we have to find the parametric representation of the straight line that passes through the points…

Q: Find parametric equations for the lines in The line through the point P(3, -4, -1) parallel to the…

A: Given P3,-4,-1r=ro+tvro=3,-4,-1,ro=3i∧-4j∧-k∧v=i∧+j∧+k∧

Q: Question 19 Let L be the line passing through the point P-(-1, 2, 2) with direction vector d-[1,-2,…

A: First find the equation is line by given points and direction.  Then assume it T and convert (x,y,z)…

Q: Complete the parametric equations of the line through the points (4,-8,1) and (-7,2,-2) x(t) = 4 –…

A:

Q: D) Find the parametric and symmetric equations of the line through the points(1, and (-5, 4, 2).

A: Given query is to find the equation of the line.

Q: Find parametric equations for the line segment joining the points (-7, 6) and (5, 3). x=-7+12t, y…

A:

Q: Question 2. Find the equation of the plane passing through the points (0, 1,0), (2, 1, 4), and…

A:

Q: Find parametric equations and an equation in vector form for the lines in R2 with the following…

A: Given: y=3x-1 To Find: Parametric Equation and and equation in vector form for the lines in R2 with…

Q: Find parametric equations for the line through the point P(2, - 5, - 3) parallel to the vector 31 -…

A: topic - equation of a line

Q: Find parametric equations for the line through P(8, −7, 9) perpendicular to the vectors A = ⟨3, −1,…

A: NOTE: Refresh your page if you can't see any equations. . the given point is  given vectors are

Q: Complete the parametric equations of the line through the point (6,-6,8) and perpendicular to the…

A: Line passing through the point 6, -6, 8 and perpendicular to the plane 7x+2y-3z=-8. Since the line…

Q: Problem 3. A plane, P, in R contains the point (-5; –-1; –3) and has normal (2; -4; 2)". Find the…

A: Given that: The point is: (-5, -1, -3)and the normal is: (2, -4, 2)T

Q: Find the parametric equations of the line perpendicular to l1 and l2 that contains the point (-1.…

A: We have to find equation of a line which is passes through the point (-1,-1,-1) and Perpendicular to…

Q: Question 11 (a) Find an equation of the plane passing through the points (0, 1, 0). (-1, 3, 2), and…

A: Given points are x1,y1,z1=0,1,0 , x2,y2,z2=-1,3,2 and x3,y3,z3=-2,0,1

Q: Questions 1 - 5. Consider the plane that goes through the point (4, 1, 3) and is orthogonal to…

A: Given that the plane that goes through the point (4,1,3) and is orthogonal to vector (2,3,1) . Here…

Q: Find an equation of the plane indicated in the figure. 4 Equation: Y 4 4

A: Equation of plane contains following points, (4,0,0), (0,4,0), (0, 4,4) and (4,0,4)

Q: Give the general equation of the plane containing the point (3,-1,4) and 2-2 -3 4. | perpendicular…

A: given plane pass through the point(3,-1,4)

Q: 4. (a) Find a parametric equation and symmetric equation of the line that pases through the point…

A: We have a point P(2,-1,3) and a vector  i^+2j^-3k^ We have to find a parametric equation and…

Q: The angle and the parametric equations for the intersect line between planes a + y = 1, and 2r+y-2z…

A: Given, x+y=1, 2x+y-2z=2 we know angle between two plane is…

Q: Find the parametric equation of the line joining the pointsA(-5,-3,0) and B(7,1,4)

A:

Q: Problem 7. Let Q(3, 1, -6) and let I be the line passing through the point Q and perpen- dicular to…

A: We have to find the equation of line L.

Q: HW Problem 1: Find the standard equation of a plane that contains the point (1,2,3) and that is…

A: Result used: If the normal vector of the plane is n→=a,b,c, then the plane equation can be written…

Q: Problem 1: Let P, be the plane defined by the equation 2x – 8y + 5z = 2 and let P2 be the plane…

A:

Q: Find parametric equations for the lines in The line through P(-2, 0, 3) and Q(3, 5, -2)

A: To find the parametric equation for PQ

Q: Find parametric equations for the line containing the points P(0,2,0) and Q(1,3,5).

A:

Q: Question 2. (a) Prove that the lines with parametric equations: x = 1+t, y =1+ 6t, z = 2t and x = 1+…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: QUESTION 1 For the parametric line L: x =4+t, y y =3+t, z=D3+2t and the plane P: -y = x+ 2z + 2,…

A: Compute the direction ratios of both the line and the normal of plane.

Q: Find parametric equations for the lines in The line through P(1, 2, -1) and Q(-1, 0, 1)

A:

Q: Find parametric equations for the line in which the planes 3x - 6y -2z = 15 and 2x + y - 2z = 5…

A: Equation of plane - 1,3x-6y-2z = 15 Normal vector of plane 1 = n1 = 3,-6,-2…

Q: Example 6: Determine whether the planes 3x+ y- 4z = 3 and -9x-3y+12z= 4 are | orthogonal, parallel,…

A:

Q: Problem 2. Find an equation for the plane that passes through points (1,4, 1), (1, 7,3), (3, 9, 1)

A:

Q: 6) Find parametric equations for the line through P(0, -2,-2) and Q(1,1,0).

A:

Q: 2. Give the parametric system of equations of the line given by the equations: 2x = 4 – 3y = ±1 Give…

A:

Q: QUESTION 1 For the parametric line L: x = 4+t, y = 3+t, z= 3-2t and the plane P: -y= x+ z + 2, then…

A: topic : line and plane line and plane are parallel to each other

Q: Question 10 Find equations for the planes: a) Passes through P(1,–1,–3) parallel to the plane 3x + y…

A:

Q: QUESTION 4 Consider the points P =(0,0,0), Q=(4,1,1), and R=(3,1,-2) in xyz-space. An equation of…

A: Given: P=(0, 0, 0)Q=(4, 1, 1)R=(3, 1, -2)

Q: Problem 6. Let P(1, -2, 4) and v = (3, 1, –5), and let l be the line passing through P and in the…

A:

Q: Question 1 Find the equation of the plane through points P1(-2,1,4), P2(1,0,3) that is perpendicular…

A:

Q: What is the parametric equations of the line through (2,2,2) parallel to the x- axis ? a) x = 2, y =…

A: 7) The Parametric equations of the line through (2, 2, 2)  parallel to x-axis is given…

Q: Example 3: Find the parametric and symmetric of the line passing through the point (-3, 5, 4) and…

A: Here, the given equation of the line is: x=1+3t,y=-1-2t,z=3+t Therefore, the direction vector is:…

Q: The angle and the parametric equations for the intersect line between planes a+y = 1, and 2r +y - 2z…

A:

Q: Problem 7 Find the distance from the point to the plane. (1) (6,0, –6), x – y = 4 (2) (3,0, 10), 2r…

A: Find the distance from the point to the plane. (1).   (6,0,-6) , x-y=4 We know that,   The distance…

Q: Find parametric equations of the line through the given points. (a) (2, −3, 1), (4, 2, 5) (b) (−3,…

A: The parametric form of a line passing through two points px1,y1,z1 and Qx2,y2,z2.Fix P-base…

Q: 13. Given the points A(3,5) and B( – 3, – 7), find b. the parametric equations of the line.

A:

Q: Find the parametric equation of the line through (1, 0, -2) and parallel to the line % (x – 4) = ½…

A: according to our guideline we are supposed to answer only the first question if you want any…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.