33) Given point P(1,2, 3) and vector n= î + ĵ , find point Q on the x-axis such that PQ and în are orthogo 34) Show there is no plane perpendicular to n= î + ĵ that passes through points P(1, 2, 3) and Q(2, 3, 4). 35) Find parametric equations of the line passing through point P(-2,1,3) that is perpendicular to the

Q: Lo and Li are lines in 3-space whose parametric equations are Loix = x0 + aot, y = yo + bot, z = zo…

A:

Q: Let S be the plane with equation 2x - 3y + 4z = 1. Find parametric equations of a line that goes…

A: Explanation of the answer is as follows

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

A:

Q: fficients of x, y, and z in the given equation of the plane. ..... z= -7+ 9t. pe expressions using t…

A: Find parametric equation.

Q: The unit vector of the PQ (of point P(-3, 4, 1) and terminal point Q(-5, 2, 2)). - The angle between…

A: here we have

Q: 1 Find equation of plane which is containing Points A(2,1,1) and B(7,5,2) and normal to 2 x - 3y -…

A: We have to find the required plane

Q: The plane with normal vector (0, – 2, – 4) containing the point (-7,4,-3) has equation Aæ + By + Cz…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: 4. Find parametric equations of a line passing through (1, 2, 3) that is parallel to the plane…

A:

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

A:

Q: Is there a plane that contains the two lines with parametric forms ⟨2t, 3 − t, −3 − 2t⟩ and ⟨1 + s,…

A: Given: L1 and L2 be the two lines in the  parametric forms L1 :    x = 2t          y = 3 − t       z…

Q: Find the parametric equation of the line that passes through point P(2,3,4) and is perpendicular to…

A: To Determine: Find the parametric equation of the line that passes through point P(2,3,4) and is…

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: Find parametric equation of the line segment ( L1 ) between the points P(1, 8, 9) and Q(5, 9, 18).…

A: To find the angle between two lines

Q: Find a set of parametric equation of the line through the point (-2, 0, 3) parallel to the vector v…

A:

Q: Find parametric equations of the line through the point (8, 3, 4) that is parallel to the plane -2x…

A: First find vector normal to plane Write equation of line

Q: Find parametric and vector equation for line segment which  reach (2, 2.4 , 3.5) point and parallel…

A: The parametric equation  of a line segment in three variables is given by the expression: Here, is…

Q: Find parametric equations for the line pass- ing through the point P(2, –1, 4) and parallel to the…

A: Given, The line is passing through the point  P 2, -1, 4  and parallel to the vector 1, 4, -2. We…

Q: Determine whether the solution space of the system Ax = 0 is a line through the origin, a plane…

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: Find parametric equation of the line joining points P{(2,4, –1) and P2(5,0, 7). Where does it…

A: To do this we need the vector V→ that will be parallel to the line. This can be any vector as long…

Q: Find all point cs) 2= 8- 3x2- 2y2 マh where the fameyent plane orlhugana l i's to とk 2ihe. X 2-31,…

A:

Q: Find a set of parametric equations for the line passing through the point (8, 0, 9) that is parallel…

A:

Q: Choose the parametric equations that represent the line segment that goes through the points (1,4,…

A: Given points x0,y0,z0=(1,4,-5) and x1y1,z1=(2,2,-1)

Q: Find parametric equation of the line passing through point (4,2) and parallel to vector 7 = -i+5j.

A: Given: A line passes through the point (4, 2). The line is parallel to the direction vector…

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

A:

Q: Find a parametric representation of a straight line through (1,1,1) and (4,0,2), and sketch it using…

A:

Q: Find parametric equations of the line through the point (5, 0,−2) that is parallel to the planes x…

A: Any point in three dimensional coordinate system will be of the form x1,y1,z1 . We can calculate the…

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 parametric and symmetric equation for the satisfying the given condition. 1. Through the…

A:

Q: Determine whether the solution space of the system Ax = 0 is a line through the origin, a plane…

A:

Q: Determine the parametric equations of the plane containing the point (1, -5, 9) and the line [x, y,…

A: I am going to calculate the parametric equations of the plane containing point (1,-5,9) and the line…

Q: Give the general equation of the plane satisfying the given condition. plane Σ containing the point…

A: We will find the equation of the plane Σ which is parallel to the plain 2x − 6y + 3z = 0 and…

Q: Find parametric equations for the line through p (2,3,0) and perpen-dicular to the vectors u =(1,…

A:

Q: Find 3 non-collinear points in the plane ax+by+cz+d=0. (Hint: Set two variables to zero for each…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Find a set of parametric equations and symmetric equations of the line ` con- taining the point P(1,…

A: Given Point is (1,-2,3) And Plan is : 2x-y+3z=6

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

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: Find a set of parametric equations for the line passing through the point (7, 0, 2) that is parallel…

A: We are asked to find the equation of the line.

Q: Give a vector parametric equation for the line through the point (−1,−1) that is perpendicular to…

A: Vector equation of line which passes through point r0 and perpendicular to line a+bt,c+dt is given…

Q: Give a vector parametric equation for the line through the point (4, 0, -5) that is parallel to the…

A:

Q: Find parametric equations for lines passing through point Pand parallel to vector n: (а) Р(3, — 1,…

A:

Q: (4,-) Find the orthogonal coordinates of point P in a plane whose polar coordinates are

A:

Q: Determine whether the solution space of the system Ax = 0 is a line through the origin, a plane…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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: Find parametric equations of the line through the point (8,3, 4) that is parallel to the plane -2x +…

A: The parallel line through the point has the vector equation L = < 8,3,4 > + t < a, b, c…

Q: The angle and the parametric equations for the intersect line between planes x + y = 1, and 2x + y–…

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.