Sketch the lines in Exercises 45–48 and find Cartesian equations for them. Зп 45. r cos (0 = V2 46. r cos (0 + 47. r cos (0 - =) rem (0 + 3) = 2 3.

Q: Find a parametric representation of the line through the points P(1,-1,2) and Q(3,1,8).

A: The parametric equation of line through the points x1,y1,z1 and x2,y2,z2 is given by  x=x1+tx2,…

Q: Find parametric equations for the line whose vector equation is given (a) (x, y) = (3, –5) + t(1,…

A: A)x, y =3, -5 + t 1, -2x, y =3, -5 + t, -2tx, y =3+t, -5-2t Parametric equations of the line:x= 3 +…

Q: A straight line has vector equation given by r=(1-A)i+(3+2A)j.How far is this line from the origin?

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

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Q: Find the angle between the planes whose vector equations are 7-(2i + 2)- 36) =57-(3i -3) + Sk) = 3…

A: The solution to the the given question is explained below.

Q: The unit vector in 2-space that makes an angle of π/3 with the positive x-axis is _____

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Q: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(-4, 8, 0),…

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Q: Find the equation for the plane through the point Po = (7,2,3) and normal to the vector n= 4i + 6j +…

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Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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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 the parametric equations for the line segment from (5,-1,1) to (5,4,3)

A: The given points are 5, -1, 1 and 5, 4, 3. The parametric equation of a line segment joining the…

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: Parametrize the line segment joining the points P(1, 2, 0) and Q(1, 3, -1).

A: We know that equation of line passing through the points (x1,y1,z1) and (x2,y2,z2) is

Q: Find an equation of the plane that passes through the point P(-4, -5, 4) and has the vector n =…

A: Plane passes through the point P-4, -5, 4 and has the vector n=-4, 9, 4 as a normal.

Q: Find the parametric equations of the line through the point P(1, 2, 4) and parallel to the vector .

A: use the parametric form  of line .

Q: Describe all points Q = (a, b, c) such that the line through Q with direction vector v intersects…

A: Given: To Find: All points Q = (a, b, c) such that the line through Q with direction vector v…

Q: Give the terminal point of the position vector of u= (3,4). Clearly show why your answer is…

A: Given that Position vector of u→=3,4 So, graphically it is as below:

Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

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Q: Find a vector equation for the line segment connecting the points P = (-9,–6, 8) and Q = (-15,…

A: We have to find a vector equation for the line segment connecting the points P=-9,-6,8 and…

Q: Find the distance from the point to the given plane. (1, -2, 4), 3x + 2y+ 6z= 5

A: Given : Point : 1,-2, 4 Plane : 3x+2y+6z = 5

Q: Find the parametric equation of the line through the points (−3, −2, 1) and(−1, −3, −1)

A: Given:

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

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Q: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

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Q: Give a vector parametric equation for the line that passes through the point (–2, 1, –2), parallel…

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Q: Give a vector parametric equation for the line through the point (4, 2) that is perpendicular to the…

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Q: 7. Give the terminal point of the position vector of ü= (3,4). Clearly show why %3D your answer is…

A: Concept: A vector is a directed line segment with an initial point and a terminal point. Vectors are…

Q: 3) Find a vector equation and parametric equations for the line segment that joins (-2, 4, 0) to…

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Q: Find the distance from the point to the given plane. (1, -3, 4), 3x+2y+ 6z = 5

A: Distance from point to plane formula If Ax + By + Cz + D = 0 is a plane equation, then distance from…

Q: Find an equation of the plane through the point (29,-37,46) and with normal vector 14i+19j–17k.

A: we have to find an equation of the plane passing through the point (29,-37,46) and with normal…

Q: Determine the vector and parametric equations of the line through A(6,2,5) and B(9,2,8)

A: Given points , A(6,2,5) B(9,2,8) Therefore a=6i+2j+5k b=9i+2j+8k

Q: Give the parametric and symmetric equations of the line that passes through the point (4, –3,5) and…

A: we have to find the equation of line which is passes through the given point and perpendicular to…

Q: Find the vector parametric equations for the line. in the direction of the vector 4 i – 3j- 3k and…

A: Equation of the line passing through a given point a,b,c and in a given direction l i+m j+n k is…

Q: Find parametric equations for the lines in The line through (2, 3, 0) perpendicular to the vectors u…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find the parametric equations of the line containing the point (-2,1,2) and parallel to the vector…

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Q: Find parametric (or vector) and symmetric equations of the line which pass through the points P,…

A: P11, 4, 6 & P22, -1, 3. Vector equation of a line passing through two points with position…

Q: Find an equation of the plane that passes through the point P(-3, -2, 3) and has the vector n = (-7,…

A: Find an equation of the plane that passes through the point P(-3, -2, 3) and has the vector n = (-7,…

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…

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Q: Give a vector parametric equation for the line through the point (-2, –2) that is perpendicular to…

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

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Q: Find the equation for the plane through the point Po = (2,7,6) and normal to the vector n= 3i + 5j +…

A: Given:-normal, n=3i+5j+6kpoint on the plane, P0=2, 7, 6let (x, y , z) on the plane vector (x-2)i+…

Q: Parametrize the line segment joining the points P(-3, 2, -3) and Q(1, -1, 4)

A: we have to parametrize the line segment joining the points P(-3,2,-3) and Q(1,-1,4)   as we know…

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, −1,…

A: Find a  vector equation and parametric equation for the line joining P and QP (1,-1,5) and Q (5,2,1)

Q: Find a vector equation and parametric equations for the line segment that joins P to Q, given P(0,…

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Q: Show that the equation of a straight line in space, represented in the Cartesian basis, is given by…

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Q: Give the parametric and symmetric equations of the line that passes through the point (5,−1,3) and…

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Q: In Cartesian coordinates, the position vector at point (3, 20, 1) is represented by…

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