Find equation of Plane that an contains the vector:<-l,1,-1> and 1-6 and Z=36

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

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Q: Find equations for the planes The plane through A(1, -2, 1) perpendicular to the vector from the…

A: The normal vector of the plane is given by A(1,-2,1)  The point of passing is (0,0,0). The equation…

Q: Find eguation of a Plane that an contains the vector: and and Z=3E

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Q: snip

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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: Write a vector of magnitude 5, parallel to the plane 3x + 4y + 5z = 10 and perpendicular to the…

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Q: Find two vectors in opposite directions that are orthogonal to the vector        u = −(1/4)i + (3/2)…

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Q: Find an equation of the plane that passes through the point (0, 0, 0) and is perpendicular to the…

A: The direction ratio of n = −3i + 2k is (-3,0,2) Given that that plane is perpendicular to n = −3i +…

Q: Find the distance of point A(23.2) from the line that passes through the origin and parallel to the…

A: given point A 23 ,2 and line passes through orgin and parallel to the vector v =&lt;1,3&gt;

Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

Q: Express the vector in terms of the unit vectors i and j. 4) (4,

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Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1, √5). Find the coordinates of the vector QS…

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Q: Determine the vector equation of the plane 5x – 2y + 3z + 24 = 0. Verify mathematically that your…

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Q: Find the unit vector that has the same direction as the vector v. 31

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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 vector v with the given magnitude and in the same direction as vector u. |V| = 7, u = (3, 4) V…

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Q: The plane contains the point (−2, 3, −1) and is normal to the vector 3i − 2j.

A: Given: point -2,3,-1   and vector 3i-2j

Q: Determine a unit vector perpendicular to the plane a =21-6j –3k and b=4i+3j – *

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find parametric equations for the line whose vector equation is given. (а) (т, у) 3 (6, —5) + t(1,…

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Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: Find an equation for the plane that passes through the point (3, -2, 1) normal to the vector n = 2i…

A: Given:A point (3, -2, 1) normal to the vector n = 2i + j + kThe normal vector can be written as,

Q: Find the equation for the plane through the point Po = (2,2,7) and normal to the vector n= 8i + 3j +…

A: Equation of plane passing through point P(x0,y0,z0) and normal to vector n=ai+bj+ck is given by:…

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

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: What is the unit vector with the same direction as the vector v = 2i - 7j? Write as a linear…

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Q: Find a vector V of a magnitude equals 14 and perpendicular To the plane in space which includes the…

A: Explanation of the answer is as follows

Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

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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 a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Two vectors of magnitudes A=3 and B=3v2 are lying on the xy plane as shown in the figure. What is…

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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: = ( The U 3 is a unit vector in V13' V13 .(2, 3) the direction of

A: We know a unit vector in the direction of vector U→ is given by : U→=U^U^

Q: Consider the vector v = (2, y) in R?. If you rotate the vector by 90-degrees counter-clockwise, then…

A: Given,   v=2,y   in ℝ2.

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

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Q: Find the component form of the vector v given ||v|| 12 following the direction of u (3, –5) %3D

A: The vector v in direction of u can be found  blew step.

Q: Find a vector parametrization of line through P = (9, 8, 3) in the direction v = (4, -8, 6). %3D…

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Q: e part of the plane with vector equation r(u, v) = (4 + v, u – 3v

A: Here we have to find the area of the part of the plane with vector equation r(u,v)=4+v, u-3v,5-4u+v…

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

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Q: Explain why the vector 2u × 3v points in the same direction as the vector u × v.

A: Consider the vectors: u=x1i^+x2j^+x3k^v=y1i^+y2j^+y3k^

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(1, −1,…

A: Find a  vector equation and parametric equation for the line joining P and QP (1,-1,5) and Q (5,2,1)

Q: Find a vector equation and parametric equations for the line segment that joins P to Q, given P(0,…

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Q: Find parametric equations for the line whose vector equation is given. (а) («, у) %3D (3, —3) + t(1,…

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Q: write the equation of the plane passingthrough P with direction vectors u and v in (a) vector form…

A: P=(0,0,0) , u=212 and v=-321we have to find the equation of the plane passing through P with…

Q: Find a unit vector that is parallel to the line x=1+2t, y= 1-3t, z= -2+t. 3 i+ 14 रंचा रत्र 1 -k 3…

A: Given line is                                           x=1+2ty=1-3tz=-2+t Point on the line is (1,…

Q: Find the horizontal and vertical components of the vector u that has magnitude |u|=4 and direction…

A: Given that, the magnitude is |u|=4 and the direction angle is α=20∘

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.