Find the vector form of the equation of the line in R2 that passes through P = (2, -1) and is perpendicular to the line with general equation 2x - 3y = 1.

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

A: Equation of a line passes through  x1, y1, z1 having direction ratios a, b, c is, x-x1a=y-y1b=z-z1c

Q: 1. What is the vector and parametric forms of the equation of the line passing through points…

A: This question can be solved using the concept of vector and parametric equation of line passing…

Q: Write down the position vectors of any two points on the line ˜ r · (3i − 4j) + 2 = 0 and hence find…

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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 an equation of the plane through the point (2,1,-3) with normal vector 2i-3j+k. Determine the…

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

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Q: What is the Direction vector for the line with Cartesian equation 3x + 2y-1= 0

A: Any line in two-dimensional Euclidean space can be described as the set of solutions to an equation…

Q: Find an equation of the plane through the point and perpendicular to the given vector. (8, 2, 3)…

A: We will find an equation of the plane through the point (8,2,3) and perpendicular to the given…

Q: Reflect the vector (-3, 5) across the line y=x

A: The vector is (-3,5)

Q: Find a vector equation with parameter t for the line through the points (-1, –7, –4) and (-6, 8, 2).…

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Q: Write a vector equation for the line segment from P to Q. 4

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Q: 1. Give the vector equation of a line perpendicular to the line L: x= 21-1, y=-31, 1 e R. Are there…

A: Given line: l:x=2t-1, y=-3t, t∈ℝ To find the other line The vector equation of the line is…

Q: Find the equation of the plane through the point (-3,2, 0) and perpendicular to the vector (1,-2,5).

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

Q: Find a vector equation for the line through the point Pla,-1,0,3) that is orthogonl t the hyperplane…

A: Suppose a line passing through the fixed point with position vector a and parallel to vector b, then…

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: Find the vector equation of the line, L that passes through the points P (2, -2, 8) and Q (10, 8,…

A: Given query is to find the equation of the line passing through indicated points

Q: Find the equation of the plane containing the point ( – 5, – 10, 9) and the two vectors and -

A: Given that , Plane containing the point -5,-10,9 So , a→=-5 i^-10 j^+9 k^ And vectors are ,…

Q: Find the vector in the same direction as <1, 1, 0> whose component in the direction of <2,…

A: Let  us suppose that

Q: Find the vector equation of a line that passes through the two points A(3,9,2) and B(−7,1, −4)

A: The given points are: A=3,9,2B=-7,1,-4  Therefore, A→=3i+9j+2kB→=-7i+j-4k  To find the vector…

Q: ) Write down the position vectors of any two points on the line T·(3i – 4j)+ 2 = 0 and hence find…

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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 the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

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

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Q: a) Find an equation of the line through P(1,-2,4) with direction vector v=[2,4,-4]

A: To find the equation of line.

Q: Determine the vector equation of a line that is perpendicular to the line, p = |-4, 4, 9 + t|-1, 3,…

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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: If P1 is (1,3,-1) and P2 is (-3,2,4), find the vector equation of the line P1P2. Determine the…

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Q: Show that direction vectors of the lines x-3y+ 1 L: and 2 -2 are orthogonal.

A: Direction vector of a line x-x1a=y-y1b=z-z1c   is   <a,b,c>  So, Write the direction vector of…

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

A: NOTE: Refresh your page if you can't see any equations. . the given point is  . the given direction…

Q: Find an equation of the plane that is parallel to the vectors and , passing through the point (3,…

A: Use given parallel vectors <1,-3,1> , <4,2,0> and passing through the point (3,0,-2)…

Q: The vector equation for the line passing through the points (-4, 1,0) and (4, 4,-3) is r(1)-

A: It is given that the line passes through the points (-4,1,0) and (4,4,-3). Consider that the vector…

Q: Find a vector equation of the line that passes through A(5,-4) and B(1,-1)

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

Q: Find the vector equation of the plane taking into account that 4x - y - z = 3

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

A: Given the point P=(-4,4) and the direction vector d=11We need to find the equation of line passing…

Q: Give the vector equation of the line passing through P and Q

A: Consider the points: P=1, -2Q=3, 0

Q: Find symmetric equations for the line that passes through the point (5, -2, 7) and is parallel to…

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Q: Find the equation of the line that passes through the point (3,4,5) and is parallel to the vector…

A: The equation of a line that passes through the point: x0, y0, z0 is L=x0, y0, z0+ta, b, c, where a,…

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

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Q: Find a vector equation of the line r through D4 and perpendicular to the line s through F4 and B1.…

A: Given,D4→ = 1i ^ + 2j^ + 3k^Equation of line passing through D4→ is:x-1a= y-2b=z-3cThe above line is…

Q: Find the equation of the plane through the point (-3,2,0) and perpendicular to the vector (1, -2,5).…

A: Questions from vector calculus.

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

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Q: Find the vector equation of a line L going through the point P = (-5, -6) and parallel to the line…

A: The vector equation of line is

Q: Find the vector equation of the line passing through the point (1, 2, - 4) and x-8 y+19 z-10 x-15 у…

A: To find the equation of line perpendicular to the given lines first we find vector perpendicular to…

Q: Find the component form of the vector.

A: Consider the figure: Find the component of form of a vector v.   The component form of a vector in…

Q: Determine the vector equation for the line that is parallel to = [1,5,-7]+[2,-1,5] with the same…

A: The general equation of line in vector form is    .Then note the result : Line passing through the…

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.