Find a vector equation and parametric equations for the line. (Use the parameter t.) The line through the point (6 -5.) and parallel to the vector (1.3.-3) r(t) %3D (x(t), v(t), zít)

Q: Show all steps carefully! Given two points A(1,1,1) and B(-7,9,2)find: a) The vector equation for…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Proceed as shown below...

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

A: Given  Point : (8,-9,4) Vector : 1,5,-23

Q: 13. Given the points A(3,5) and B(- 3, - 7), find a. the vector equation of the line. b. the…

A: Here, the given points are A(3,5) & B(-3,-7)

Q: (a)i Find a vector equation and parametric equations for the line that passes through the point A(5,…

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Q: a line is parallel to the vector i+ 5j+3k and passes through the point P = (6, 2, 4), then the…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

A: Given problem:- Find a vector equation and parametric equations for the line. (Use the parameter t.)…

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) the line…

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Q: Given the parametric equations x = t1 - t2 y = 2 + t2 z = -1 - 211 + 3t2 These parametric equations…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) the line…

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Q: The position vector r describes the path of an object moving in the xy-plane. (a) Find the velocity…

A: At a point (1, 1).

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, -1, 4),…

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Q: Vector equation of the circle (x + 3)2 + (y - 2)² = 16 is: %3D (A) 7(t) = (B) 7(t) = (C) 7(t) = (D)…

A: The given equation of the circle is (x-3)2+(y-2)2=16 We have to find the vector equation of the…

Q: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

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

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Q: x- 2. Find a vector equation of a plane that contains the line y+2 -2 and the point A(1,2,1).

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Q: Find a vector equation and parametric equations for the line that passes through the point (2,1,-3)…

A: We have to find out

Q: (a) Determine the vector and parametric equations of the line containing points E (-1, 5) and F (6,…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given that , Point =0,0,0 and parallel line r=3+2t , 7-6t , 5+4t find vector and parametric equation…

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, –1, 7),…

A: Please refer the attached image for complete solution.     Please refer the attached image for…

Q: The vector equation of two lines , and 4 are 1+x 2- -3+2 and 4 a-y= Given that/, and /, intersect at…

A: Solution (i): Value of a Given lines are, (1+x)/2​=(2-y)/3​=(−3+z)/4​=(r1​)(say)     .... (i)So,…

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, 0, 1),…

A: Given points are; P(1,0,1) ,Q(4,2,1).

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, -1, 8),…

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Q: (A) Find the unique point P on the y-axis which is on both planes. (B) Find a unit vector u with…

A: (a) ... Unique point on the  y axis on the both planes  On the y axis means, x and z=o  Which means…

Q: A line has y-intercept 11 and z-intercept -13. Find a vector equation of the line.

A: The line has y-intercept 11 and z-intercept -13. So the line passes through points A(0,11,0) and…

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

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Q: (a) Write the vector or parametric equations of the line through the point (2,0, 3) and…

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Q: An object moves in space with acceleration a(t) = 12t²i+6tj+2k. When t = 0, the object is at (1, 0,…

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Q: Find the equation of the line that goes through the point (1,3, 2) and is parallel to the line (3t –…

A: The given line equation in parametric form is x=-2+3t y=1+2t z=4+t The direction ratio is…

Q: Solve the following vector problems and parametric equations: a) Find the vector equation and the…

A: Q. Vector eqn of line passing through Prx0,y0,z0      and parallel to x, y , z is          r = Pr +…

Q: This is a two part problem. A. Find a vector parametric equation r(t) for the line through the…

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Q: х-2 у-4 Convert the symmetric equation of the line l: to the vector equation. 6. 7

A: Here we have to convert the symmetric equation of the line l:(x-2)/6=(y-4)/7 to the vector equation.

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) the line…

A: We have to find the equation

Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) The line…

A:

Q: Given the parametric equations x = t1 - t2 y = 2 + 12 z = -1 - 211 + 3t2 These parametric equations…

A: Given that, the parametric equation as, x=t1-t2y=2+t2z=-1-2t1+3t2 Here, parametric equation are…

Q: Give a vector parametric equation for the line through the point (1,2) that is perpendicular to the…

A: Here ,       given line -3-3t,3-2t    we gave to find the vector parametric equation for the line…

Q: Find parametric equations for the lines in Exercises 1–4. 1. The line through the origin parallel to…

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

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

A: Consider the given parametric equation of line 5+4t,5t−3Find the parametric equation of the line…

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

A: P0,0,0Q1,8,3for Vector equationPQ→=P+dPQ→r→t=0,0,0+t1,8,3∴ r→t=ti∧+8tj∧+3tk∧

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: u = < 0,2,2>  w = < 2,-2,0>  U× W is perpendicular to both u and w

Q: Q1: Find the vector equation, parametric equations, symmetric equations for the line that pass…

A: We need to find the vector equation parametric equation and the symmetric equations for that line.…

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

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(-8, 2, 0),…

A: The objective is to find the vector equation and parametric equation for the line segment joininging…

Q: 5. Given the points P= (2,-4,-1) and Q= (5,-4,2) in space. A) Find the parametric equations of the…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) the line…

A: We have to find the equation

Q: 12. Given the vector equation [x, y]= [3,1]+[3,-5] find a) the parametric equations b) the symmetric…

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Q: Find a vector equation and parametric equations for the line. (Use the parameter t.) the line…

A: Solve

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

A: Here, the direction vector will be =12, 103, -74. So, the vector equation will be…

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find a.…

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Q: Find parametric equations for the normal line to the surface at the indicated point. (Recall that to…

A: Let fx,y,z=x2-9xyz+y2+7z2. and given point is P1,1,1. Partially Differentiating f with respect to…

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.