Let P(1,3,5) and Q(-4, 3, –7) be points in R³. Let l be the line through P and Q. Let P be the plane on P, Q, and the origin. (d) Find a vector equation for P. (e) Find the scalar equation for P. (f) Find a linear equation for P.

Q: 2. (a) Calculate the position vector for P₁ and the displacement vector from P₁ to P₂, where P₁:…

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Q: Find the component form of the vector v, (a) write the vector using standard unit vector notation,…

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Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. -2u

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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 b.…

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Q: Find a vector equation for the plane that contains the points P, Q and R Find a scalar equation for…

A: Given points: P(2,1,1),Q(0,4,1),R(−2,1,4) and S(1,5,−4) Equation of a plane in cartesian form…

Q: Which of the following is the vector equation of the line through the point (1,2,3) and parallel to…

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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…

A: Given, The parametric equation of the line D passing through A and parallel to vector v is  x =…

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

A: point = (3,5,-7)n=0 i +1 j + 0 kCartesian equation of plane is Ax+By+Cz+D=0(A,B,C)=( 0,1,0)(x,y,z) =…

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: 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: A particle is moving along the curve having the vector equation R(t) = ti+t²j+ tk. Find the vectors…

A: The given position vector is  Rt=t i + t2 j + t k.   The velocity vector is given by Vt=R't=i+2t j…

Q: Find the point A (a, a, 0) on the line y = x in the xy-plane, such that the vector AB is…

A: Solution is given below:

Q: Find the component form of the vector v and (b) sketch the vector with its initial point at the…

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Q: Find the equation of a line in vector form that is parallel to 3x−2y+z= 4, passes through the point…

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

A: Given: (2,3,-6) Perpendicular to j vector

Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: 4u.(5v - 3w)

A: Given: u = -i + j, v = 3i - 2j, and w = -5j

Q: 10.Determine the vector equation of the plane that contains the origin and the intersection of:…

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

A: Given that the point that posses through the line and the line perpendicular to the plane is, P 0 =…

Q: Find a vector equation of the line passing through the points P(-2, 1, 3) and Q(3, 0, -2). 1+t ,te…

A: The vector equation of the line passing through the points A(x1,y1,z1) and B(x2,y2,z2)  is given by;…

Q: Let x = p+ su +tv be the vector equation of a plane in R³. Then the plane passes through the origin…

A: Vector equation of a plane:

Q: M contains the point with coordinates (0,0,1) 2 M is orthogonal to the vector 0

A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

Q: Find the equation of the plane E passing through the point P(2,3,1) and parallel to the vectors K =…

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Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

Q: Find the equation of the plane that passes through the point P(1, 0, 2) and contains the line whose…

A: Hi there, At a time we can answer only one question. So, I have answered first one (#6).

Q: Find the vector equation that represents the curve of intersection of the paraboloid z 2x2 + y and…

A: z=2x2+y2  & x=ey We can see that y can be represented in terms of x.

Q: (g) We have a set of vectors: U1 = £1 - L2 + £3 2e1 + £3 = +£2 + 2e3 with which we are going to use…

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Q: Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

A: The plane is perpendicular to the line, then the direction vector of the line is normal to the…

Q: For the given vector function below, find the equation of the plane that contains the osculating…

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Q: If a line is parallel to the vector 3i +2j+ 1k and passes through the point P = (1,3,8), then the…

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Q: Consider the vector y = [1 2 3]. Find the orthogonal projection of y onto the plane x, - 2x2 + 4x3 =…

A: Given vector is y=1,2,3 Given plane is x1-2x2+4x3=0 Normal vector to the p[lane is n=1,-2,4…

Q: га- Find an equation that describes all values of a, b, and c for which the vector w = |b| is NOT a…

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Q: Find a vector perpendicular to the graph of z = - 3 x2 + 9 y2 – 7 x y at the point (8, 2, -268).

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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: find the two-dimensional vector equation of the line r(t) = a +t*m such that - r(0) has norm 8 and…

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Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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Q: Find the second and the third components of a vector n normal to the plane with the equation 7x +…

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Q: Let / be the line through the point with coordinates (1,0,0) in the direction of the vector -2 .…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: 5u.(3v - 4w)

A: Given: u=-i+j, v=3i-2j and w=-5j

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 the vector joining the points P1= (-3, 1) and P2= (5, 2) %3D %3D in terms of i and j.

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( – 1,…

A: find the explanation below

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 vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y and…

A: The given curves are: z=4x2+y2     and     x=ey

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.…

A:

Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), 0(2, 0, – 1), and…

A: It is given that the plane contains  P(1,0,0), Q(2,0,-1) and R(1,4,3). Let, Equation of plane…

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.