Find the vector and parametric equations for the line through the point P(4, -2, -4) and parallel to the vector 4i – lj+ 4k. Vector Form: r = -4 ) +t( , 4) Parametric form (parameter t, and passing through P when t = 0): x = x(t) = y = y(t) = z = z(t) =

Q: Find the vector and parametric equations for the line through the point P(2, 2, -2) and orthogonal…

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Q: Find parametric equations for the line described below. The line through the point P(-1, -1, 5)…

A: Question 17 In general, we know that the equation of the line passing through the point (x1, y1, z1)…

Q: 3 2) Determine the vector, parametric and cartesian eguation ef the line passing through-the…

A: Given: Passing point P0(1,3,2) Parallel vector V=(1,1,1)

Q: A) Find the parametric equations for the line through the point P = (3.-5, 1) that is perpendicular…

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

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

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Q: A line initiated from (1,0,2) and parallel to a vector 2i + j what is the parametric equation of the…

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –6) + t(1,…

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Q: Find parametric equations for the line through (- 1,6, - 1) perpendicular to the plane 7x+ 5y + 5z =…

A: to find the parametric equations for line passing through (-1, 6, -1) and perpendicular to the…

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: 1.Find the vector equation and parametric equations of the line passing through the point P(5, 6, 7)…

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Q: 2. The line in R³ through the point Po(xo; Yo, 2o) and parallel to the vector v = parametric…

A: NOTE:- By bartleby rule, only question number (2) has been answered. The line in ℝ3 through the…

Q: Find parametric equations for the line described below. The line through the point P(1, 1, -2)…

A: we have to find

Q: Find the vector and parametric equations for the line through the point P = (-1, 4, −4) and the…

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

A: Answer

Q: Determine vector and parametric equations for the line in R that passes through the points A(1,0, 1,…

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Q: (a) Find a vector parallel to the line of intersection of the planes -x + 3y + 4z : 0 and -x - 3y –…

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Q: Find the vector and parametric equations for the line through the point P(-5, 3, -1) and the point…

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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 the vector and parametric equations for the line through the point P(3, 1, 5) and the point…

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Q: 1. Find both the vector equation and the parametric equations of the line through (−3​,5​,6​)and…

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Q: (1 point) Given a the vector equation r(t) = (4 + 4t)i + (1 + 1t)j + (1 + 4t)k, rewrite this in…

A: See below the answer

Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

Q: Find the vector and parametric equations for the line through the point P = (-4, –4, 5) and the…

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Q: The side of S is given by x² + y = 16, and its height is 4. (a) Give a parametric equation, r(t) for…

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Q: Find a parametric equation for the line through the point ( – 1, – 1,2) and perpendicular to the…

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Q: Find the vector and parametric equations for the line through the point P(1, 1, -3) and orthogonal…

A: Given: Point= (1, 1, -3) Orthogonal to plane: 3y-4x+2z=3 The direction vector for this line is v=…

Q: Find both the vector equation and the parametric equations of the line through (3,3,1) that is…

A: If line perpendicular to both lines the direction vector perpendicular to both parallel vectors of…

Q: Find the vector and parametric equations for the line through the point P(-2, 1, -5) and the point…

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Q: Find the vector and parametric equations for the line through the point P(-2, 4, -3) and parallel to…

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Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + 4y +…

A: Equation of line normal to graph of functions f(x) is :  r<t> = <x0,y0,z0> +…

Q: Find:   a) the parametric equation of the line determined by points A(1,0,2) and B(2.2.1). b) the…

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Q: Find a parametric form for the line through the point (0, –7, -9) and parallel to the vector 6i – 7j…

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Q: b) Find parametric equations of the plane (P) containing the point P(1,-2, 0) and the vectors û and…

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Q: Find parametric equations for the line through (- 4,6,1) perpendicular to the plane 7x + 3y + 9z =…

A: Note that, a vector which is perpendicular to the plane ax+by+cz+d=0 is (a, b, c). A parametric…

Q: Consider the line l in R³ given by the parametric vector equation 3 1 -2 -1 and the plane described…

A: Given that the line l in R3 given by the parametric vector equation and the plane described by the…

Q: Find the vector and parametric equations for the line through the point P= (3,0, –1) and the point Q…

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Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (2, –5) + t(1,…

A: Parametric equation of the line, <x,y,z>=<a,b,c>+t<p,q,r> , t is a scalar is given…

Q: Find the vector and parametric equations for the line through the point P(-4, -1, -3) and orthogonal…

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Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A: According to question given thatplanes equation 4x-y-3z=6-5x+4y-4z=3

Q: Find parametric equations for the line through (- 3,1,2) perpendicular to the plane 7x + 9y + 9z =…

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Q: Find the vector and parametric equations for the line through the point P(-1, 3, 4) and the point…

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Q: Find the parametric equations for the line through the point P = (-1, 4, -4) that is perpendicular…

A: Normal vector perpendicular to the plane 2x−4y−2z=1 is: (2, -4, -2) The line passes through P = (-1,…

Q: Find parametric equations for the line whose vector equation is (a) (x, y) = (3, –5) + t(1, –2) X =…

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Q: 47. Determine the vector and parametric equations for the line passing through the points P(-1,-3)…

A: We’ll answer the 47th question since we answer only one question at a time. Please submit a new…

Q: Find a set of parametric equations for the line passing through the point       (1, 0, 2) that is…

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Q: Find a vector equation and parametric equations in t for the line through the point and parallel to…

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Q: The line L is parallel to the plane x+y+z=2 and is perpendicular to the vector (-1,1,–2). If the…

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Q: Suppose F(x, y) = x?i+ y?j and C is the line segment segment from point P = (-5, –5) to Q = (-3,…

A: Given data: The given expression for the vector is F→(x,y)=x2i→+y2j→. The given first point is…

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.