Give the equation of the line in vector form, parametric form and symmetric form. The line through the point (1,-5,0) and parallel to the line given by r(t)=( 8–3t, –10+9t, –1–t >

Q: Find a parametric representation of the solution set of the linear equation.3x − 1/2y = 9

A: Given equation is Where x and y are unknown.

Q: Find the vector, parametric, and symmetric equations of the line which passes through the points A =…

A: Given points are: A=3,1,-1 and B=7,0,1 To find the vector, parametric, and symmetric equations

Q: Find the equation of a plane that is perpendicular to the vector – i+ 2j+ 2k and passing through the…

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Q: Find a vector parametric equation r(t)|for the line through the points P = (-3, –2)|and Q = (-5,…

A: According to the problem, we have

Q: Find the vector equation for the line of intersection of the planes 5x +y-3z= -3 and 5x + z = -1 r =…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x= 2+3t y…

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Q: Write the line through p=(5,2,2) in the direction of v¯=⟨3,5,0⟩ in vector parametric form: L(t) =…

A: We know that the equation of line passing through the point P in the direction of v→ is…

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

A: we have to find

Q: If a line is parallel to the vector 2i + 7j + 10k and passes through the point P = (6, 10, 5), then…

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Q: Write the equation of the line passing through P with direction vector d in vector form and…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find a parametric representation of the solution set of the linear equation.2x − 4y = 0

A: To find the parametric representation of the solution set, solve the given equation for the value of…

Q: Find an equation of the plane. The plane that passes through the point (1, 3, 5) and contains the…

A: Given linex=5t , y=1+t , z=3-tDirection vector of this linev⇀=5,1,-1coefficients of t

Q: Give the equation of the line in vector form, parametric form and symmet The line through the point…

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Q: d) A scalar equation of a line that goes through T(2, -5) and is perpendicular to the line 3x - 6y =…

A: The given line is: 3x-6y=5⇒6y=3x-5⇒y=3x-56⇒y=12x-56 which has a slope m=12.

Q: Find a plane containing the point (5,-6,-3) and the line x(t) y(t) z(t) = = = - 4 - 7t 1 -8t 3 - 4t

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Q: Let Q(0,-1,1) be a point in space and let u have the line L whose equation is L: 3- 3x = 1 – 3 y…

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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: Which of the following is a direction vector for the plane with Cartesian equation 3x -2y - 5z + 3 =…

A: To find a direction vector for the given plane. The general form of plane with cartesian equation…

Q: 1. Write vector and parametric equations of the line. a) parallel to the line x+6y = 1 and through…

A: Parametric and vector equation of line

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: 5) Write the equation of the line through the points P(1,3,7) and Q(2,5,11) in: a) Vector form b)…

A: topic - equation of line through two points

Q: Find parametric equations for the line through the points P(-1,- 1, -4) and Q(-4,-7,7). O A. x-t-3 y…

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Q: give the equation of the line in vector form, parametric form and symmetric form. k) The line…

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Q: The scalar equation of the line perpendicular to (x, y) = (5, 2) +r(1, -3) through the point (2, -2)…

A: The scalar equation of a line is of the form Ax+By+C=0

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 an equation of the plane passing through the point perpendicular to the given vector or line.…

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Q: Write the scalar equation of the plane. a) perpendicular to the line [x, y, z]=[1 -2, -3]+t[5, – 4,…

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

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given the points P = (2,3,4), Q = (4,–1,5) and R = (-2,5,6) : a. Find a parametric or vector…

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Q: Which one of these is a vector equation for a line in 2-space? y = 3x + 7 =(-2, 1,0) + s(-4, 2, 1) +…

A: Given ○y=3x+7○r→=-2, 1, 0+s-4, 2, 1+t1, -1, 2 s,t∈R○3x+4y+7=0○r→=2, 1+t-1, 3 t∈R

Q: Find an equation of the plane passing through the point perpendicular to the given vector or line.…

A: Given point is (0,4,0) and normal vector is -7i+5j.

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: 4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x -…

A: Given plane is, 2x-3y+7z-4=0

Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: Find the vector form of the equation of the line inR3 that passes through P = ( - 1, 0, 3) and is…

A: Find the vector form of equation of line passing through point  P=-1,0,3 and perpendicular to the…

Q: Write vector and parametric equations of the line. a) parallel to the line x+6y = 1 and through the…

A: We know that the line equation of the line that passes through point (ro→), and parallel to vector…

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: An equation of a plane P passes through the point (0,0,3) and perpendicular to the line L:x =1– 2t,…

A: Given,          An equation of a plane P passes through the point 0,0,3 and perpendicular…

Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: Given the points P = (2,3, 4), Q = (4,–1,5) and R = (-2,5,6) : a. Find a parametric or vector…

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Q: Use the component form to generate an equation for the plane through P1(4, 1, 5) normal to n1 = i -…

A: Concept - If a plane is passing through (x0, y0, z0) and normal vector is A, B, C.Then equation of…

Q: (a) Find a parametric equation and symmetric equation of the line that pases through the point (2,…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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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 the equation of the line in vector form, parametric form and symmetric form. 11) The line…

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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: 2. Answer and show the Solution in parametric vector form. a. x, + 3x2 - 3x3 = 7 c. x, + 2x;- 3x3 =…

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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.