Represent the line segment from P to Q by a vector-valued fur P corresponds to t = 0. Q corresponds to t = 1.) P(-9, -4, -3), Q(-1, -6, -9) r(t) = Represent the line segment from P to Q by a set of parametric eauations. (Enter your answers as a comma-separated list of equations.)

Q: a line is parallel to the vector 2i +7j+7k and passes through the point P = (7, 10, 3), then the…

A: Given query is to find indicated line.

Q: Find the distance of point A(2/3, 2) from the line that passes through the origin and parallel to…

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Q: Find the new equation of the line y=x after applying the translation by the vector (2, -1)

A: New line will be shifted to 2 units right and 1 unit down.   Point on x axis (2,0) Point on y axis…

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

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Q: 3. Determine the vector equation for the line with symmetric equations*=3+22=1

A: Given: Symmetric equation of line: x-34=y+25=z-13 To find: Vector equation of line.

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

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Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² – 2x + 2y…

A: The given equation is: 2x2+2y2-2x+2y=7...(1)

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 a vector equation for the line segment from (2, -4, 6) to (5, 5, 5). (Use the parameter t.)…

A: a→=2i-4j+6kb→=5i+5j+5kn→=b→-a→=3i+9j-k

Q: Find the distance of point A(2-3,2) from the line that passes through the origin and parallel to the…

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Q: Find both the vector equation and the parametric equations of the line through (4,3,6) that is…

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Q: O Find the parametric equation of the line through the point (-3,1,6) parallel to the vector V 2i +…

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Q: 3. The line through the point (2, 2.4, 3.5) and parallel to the vector 3i+ j – k Answer + (2i+ 2.4j…

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Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Find a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

A: To find the equation of line with parameter t of the intersection of the planes  x + y + z =4 and…

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 a vector equation for the curve of intersection between the surfaces y^2-x^2=9 and 2x-3y-z=12.

A: Introduction: We can determine the vector equation of the curve formed by the intersection of two…

Q: Find a vector equation for the line segment from (2, -4, 5) to (6, 4, 4). (Use the parameter t.)…

A: Explanation of the solution is given below...

Q: Find equation of Plane that an contains the vector: and 1-6 and Z=36

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) and (5,2,4),…

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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: 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: Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2a + 2z = 1

A: Given  equation of planes 2x-2y-5z=5 2x+2z=1

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: write the equation of the line passing through P with direction vector d in (a) vector form and (b)…

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Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: 27. Are the points P(1, 2), e(7,3), and R(-2, 1) on the line with vector equation = (19,5) + s(6,1),…

A: According to our terms and conditions I have solved first question for next question repost

Q: Find the linear equation of the plane through the point (-3, 4, 3) and perpendicular to the line…

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

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Q: Write the line through p = (3, 2, 2) in the direction of v = (-1, –4, 2) in vector parametric form:…

A: We have to write the line trough p=3,2,2 in the direction of v¯=-1,-4,2 in vector parametric form.

Q: . The line (x-2z 3, y 22) intersects the plane (x+3y-:+4=0) at the point P, Find: (a) the…

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Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: Find the vector equation of the line that is perpindicular to the line q(t) = (1,2, 3) + s(2, –1, 1)…

A: Consider a point P(1+2s, 2-s, 3+s) on the vector equation of the line. The vector joining points P…

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

A: We have to write a parametric equation of the line  which is passing through the point (-1, -1)…

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

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Q: a) The line y =- 5x + 9, in VECTOR form (R?).

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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: Show that A(x - x0) + B( y - y0) = 0 is an equation for the line in the xy-plane through the point…

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Q: Find a vector equation for the line through the point P = (4, -2, -4) and parallel to the vector vv…

A: P= (4,-2,-4) is a point on the line.  And the line is parallel to v=(4,-1,4)  v is the velocity…

Q: Give a set of parametric equations for the line L4 that lies tangent to the graph of the vector…

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Q: )P=(3,2,1), then the parametric equation of the line is :   a.

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Q: Find the parametric equation of line that passes throught the point (1,-2,4) and is parallel to the…

A: The given point is (1, -2, 4) and parallel to the vector v=[2, 4, -4].

Q: 22. Determine the vector and parametric equations for the line passing through the points P(-1,-3)…

A: “Since you have posted multiple questions, we will solve the first question for you. To get the…

Q: Represent the following equation in R² by a vector-valued/parametric equations: 2x² + 2y² − 2x + 2y…

A:

Q: Find parametric equations for the line whose vector equation is given. (a) (x, y) = (4, –3) +t(1,…

A:

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

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Q: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

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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.