Find the equation of the plane that passes through the point P(1, 0, 2) and contains the line whose vector equation is r(t) = (1-t, t+2, – 3t). Write the equation in the form ax+ by+ cz = d, with all integer coefficients.

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 v parallel to the intersection of the planes - (2x + 4y + 3z) = 4 and 3x + y + z = 7.

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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: Find an equation of the plane that passes through the point P(-7,–5,5) and has the vector n = (-1,4,…

A: Given : Point P(-7,-5,5) and a normal vector n=<-1,4,2>   To Find : Equation of the plane that…

Q: Find the equation of the plane through the point with position vector 5i-2j+3k perpendicular to the…

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Q: Find the cartesian equation of the plane that is normal to the vector n = -3i – 4j+4k and includes…

A: n=-3i-4j+4k  and P(2,-7,5)

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: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

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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: Find the vector equation of the line that passes through point M(1, 1, 2), intersects the following…

A: Question is solved.

Q: Find the equation of the plane sanned by the above two vectors

A: Given: Two vectors u=223 and v=-20-3. To find: Equation of plane spanned by given vectors.

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 a vector normal to the plane with the given equation. 2x + 8y + 9z = 3 n =

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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: Determine the vector, parametric, and Cartesian (Scalar) equations for the line that passes through…

A: To find the equation of line that passes through the point A(4,-1) and is also perpendicular to line…

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: The z-coordinate of the terminal point of the vector v=-5i-19k whose initial point is (-1,-4,-5) is

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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: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

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Q: Find the scalar equation for the plane passing through the points P-(-1. 5.-1. P=(-1, 6, 5), and…

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Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)

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Q: Write a scalar equation of each plane, Given its vector equation [x, y, z] = [7, -3, 4]+s [1, -2,…

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Q: Find a vector equation for the line through the point (2, 5, 8) perpendicular to the plane 2x + 5y +…

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Q: Determine the vector, parametric and cartesian (scalar) equations for the line that passes through…

A: First, we will find the cartesian equation of the line L through the points M(-2,0) and N(3,-3).…

Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

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. The plane through the point (4, 0, -5) and perpendicular to the…

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Q: Find the value of h for which the vectors are linearly dependent

A: The given vectors are 1-14 , 3-57 , -15h The vector v3 are linearly dependent if the equation…

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: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

A:

Q: Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

A: Given: Let A(7,6,2) and B(2,14,2) be the two points the line passes through To find: vector equation…

Q: Find the equation of the plane in xyz space through the point P= (3,3,4)and perpendicular to the…

A: We need to find equation of plane.

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

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Q: Find an equation of the plane that passes through the point P(-3, -2, 3) and has the vector n = (-7,…

A: Find an equation of the plane that passes through the point P(-3, -2, 3) and has the vector n = (-7,…

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

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Q: Find an equation of the line that goes through A(0, 1, 4) and is orthogonal to the Y-axis and vector…

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Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then…

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

Q: Parametrize the line that passes through the point (1, 2, 3) rallel to the vector V = -3i +7k .

A:

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

A: find the explanation below

Q: b) Find equation of the Plane through point (1, 2, 3) parallel to the vectors V1 = 2i + 3j + k and…

A:

Q: Find a vector equation for the line that goes through the points (5,9,0) and (0, 11, 1). F(1) = with…

A: A ( 5,9,0) B ( 0,11,1)

Q: Find the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the…

A: topic - equation of a plane

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

A: Here we have to find the equation of the plane passing through the point (0,4,0) and perpendicular…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 4y – 3x +3z = -2 and z…

A: Answer

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.