4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x - 3y + 7z - 4 = 0 and which passes through the point P = (1, -5, 7).

Q: B- Find the parametric equations for the line through point (1,0) and parallel to the function f(x,…

A:

Q: What is the parametric equation of line through the point (1,2, -1) and perpendicular to the plane…

A:

Q: Find the parametric equations for the line through the point of intersection of the lines L,:x = 2…

A:

Q: Find a set of parametric equations for the line passing through the point (2, 0, 9) that is…

A: a set of parametric equations for the line passing through the point (2, 0, 9)  that is parallel to…

Q: Find a set of parametric equation of the line through the point (1, 0, 1) parallel to the line x = 3…

A:

Q: Find the scalar equation of the plane that contain the line 7 = [2,1,7] + t[0, 1, 0], t e R and is…

A: Here we will find out the required plane.

Q: The planes 4x + 4y + 3z = -15 and y - 5x - 2z = 11 are not parallel, so they must %3D intersect…

A: Given: The planes 4x+4y+3z=-15 and y-5x-2z=11

Q: Determine the parametric equation of the plane that contains the line y-3 *+2-³-² and the point…

A: Virtual find the standard form of the plane then by satisfying the parametric values we will…

Q: 3. Find a set of parametric equations for the line of the intersection of the planes 3x-3y-7z -4 and…

A:

Q: Determine the vector and parametric equations of the plane containing the point (1, -5, 9) and the…

A: Answer

Q: 2. Find the vector, parametric and cartesian equation of a plane that contains the points А(-1,0,…

A:

Q: A parametric equation of the line of the intersection of the planes x - z = 0 and x – y + 2z = 0 is

A:

Q: a b 3. Write the scalar equation of the plane with normal vector = [5,-1,-2] and passing through the…

A:

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A: What is the parametric equations of line line through the point (1,2,-1)and is perpendicular to the…

Q: Give a vector parametric equation for the line that passes through the point (3, 5, –5), parallel to…

A:

Q: 5. Find the parametric equations of the line that passes through the point (0, 1, 4)and is…

A: Given two vectors, u=2, -5, 1v=-3, 1, 4 Also, given the point, P=0,1,4 The cross product of u and v…

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 a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

A:

Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is per- pendicular to…

A: Let's find.

Q: 3. Write the scalar equation for a plane passing through (5,8,-1) and perpendicular to the line x =…

A:

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A: The objective is to find the parametric equations of the line through the point.

Q: Find the parametric equations for the line through the point of intersection of the lines L1:x = 2 +…

A: In line L1 and L2  't' is used as parameter but don't confuse with it. Different different line we…

Q: Find a parametric equation for the line through the point (6,5, - 3) and perpendicular to the plane…

A: Given plane is, 7x+4y+4z=15 Since, the line is perpendicular to the plane then the normal vector…

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: In Exercises 23–38, find parametric equations for the given curve. 30. Line through (2, 5)…

A:

Q: Derive the parametric equations of the line of intersection of the two planes: II : 2x – y + 2z = -1…

A: We need to find the vector equation of the line of intersection. In order to get it, we’ll need to…

Q: The planes 5x+y+z=−6 and 3y+5z=22 are not parallel, so they must intersect along a line that is…

A: Given planes are 5x+y+z=-6 and 3y+5z=22 find the vector parametric equation

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A:

Q: Find a set of parametric and symmetric equations of the line satisfying the following Passing…

A: We have to find the equation of the line passing through the point (1,2,-1) and normal to the plane…

Q: Find the general equation of the plane through the point (1, 1, 1) that is perpendicular to the line…

A: We know that equation of plane which passes through pointx1,y1,z1 and perpendicular to linex=x2+at,…

Q: At which point will the plane 2x + 4y – 3z = -48 and the line given by the parametric equations x =…

A:

Q: Find the parametric equations for the line through the point (0, 1, 2) that is perpendicular to the…

A:

Q: 5. Determine the scalar equation of the plane with x-intercept = 2, y-intercept = -1, and…

A:

Q: Find the set of symmetric and parametric equations of the line passing through the point P(3, 4, 1)…

A:

Q: Provide the point-normal form equation of the plane containing (1, -1, 4) and line with parametric…

A:

Q: Find the scalar equation for the plane passing through the point P-(0,-3, 2) and containing the line…

A:

Q: 1. Find the vector and parametric equations for a line passing through (7,-4, 2) and parallel to the…

A: We have to find the vector and parametric equation of the line

Q: Compute the parametric equations of the line in R3 determined by the intersection of the two planes:…

A: To obtain the parametric equations of the intersection line, use the following formulae. Let n1→…

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.

A:

Q: The planes 3x−4y+5z=−28 and 4x−2y+4z=−24 are not parallel, so they must intersect along a line that…

A:

Q: What is the parametric equation of line through the point (1,2,-1) and perpendicular to the plane…

A:

Q: The planes 5x+ 2y + 2z = 5 and 3x + 5y = -22 are not parallel, so they must intersect along a line…

A:

Q: Q2 What are the parametric equations for the line through the point (6,-3,1) that is orthogonal to…

A: We have to find the equation of parametric line

Q: Suppose a line is given parametrically by the equation L(t)=(1-t, t-4, 1-t) then the vector u and…

A:

Q: 10. Determine the scalar equation of a plane that is perpendicular to the line: |1,2, 3| + t|-2,4,…

A: A normal of a plane perpendicular to the line will be parallel to the line. So the plane is:…

Q: Derive the parametric equations of the line of intersection of the two planes: II : x – 2y + z =1…

A: Given: P1:   x−2y+z=1P2:   2x−2y−4z=4

Q: perpendicular

A:

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.