(2, -3 ,1),(2, -3 ,5) Express the space stretched by the vectors with cartesian equations.

Q: The component of the vector (-5, 0, –3) onto the vector (3, –4, –2).

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Q: Find the equation of the plane that is parallel to the vectors (1,0,1) and (0,1,1), passing through…

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Q: ASAP: find the equation of the plane that is parallel to the vectors (3,0,1) and (0,2,1) passing…

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Q: What is the size of the space stretched by the vectors {(1,0,2),(2,1,4),(1,-1,1)}?

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Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

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Q: A vector orthogonal to the plane through the points (-1,0, 0), (0, 0,-2), (2, 3, 4) is

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Q: . Find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q = (4, -2,1)…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, -2, -2), (2, 3, 4) is < 2, – 10, 6…

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Q: 2. Find the vector, parametric and cartesian equation of a plane that contains the points А(-1,0,…

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Q: Show that the vectors ⟨1, 2, 3⟩, ⟨1, 1, 0⟩, and ⟨3, 4, 3⟩ lie in the same plane

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Q: The two vectors a = (-1,2,-2) and b = (2, -4,-5), are not parallel but are orthogonal. Select one:…

A: Using algebraic operation

Q: Do the vectors (1, 0, 0), (0, 1, 0), and (2, 3, 0) lie on the same plane? Briefly explain how you…

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Q: What is equation of the plane passing through the point A(-2,-1,-3) and paralleto the vectors a=3+2k…

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Q: A plane in R'is perpendicular to the vector (4, 2, – 9), and contains the point (- 9, 5, - 8). Find…

A: A plane in ℝ3 is perpendicular to the vector 4, 2, -9 and contains point -9, 5, -8To find the…

Q: 10

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Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: The line that passes through the point (4, –2, 0) and parallel to the vector (1, 2, –3) has…

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, –2), (2, 3, 4) is

A: Query- Find a vector orthogonal to the plane through the points -1,0,0,0,-2,-2,2,3,4. Answer- Let…

Q: prove using vectors that the points (0),2 -2- (B2,0, -2, C, (2,2-,10) represent the vertices of a…

A: We have to check weather the given points are Vertices of Traingle or not.  After that we have to…

Q: The vector (3, -1, 2) is parallel to the plane 6x – 2y + 4z = 1. - %3D

A: Use formula to calculate equation of plane

Q: Give the parametric and symmetric equations of the line that passes through the point (2,6, –1) and…

A: To find equation of line passing through the point 2,6,−1 and perpendicular to both vectors −4,3,−5…

Q: Find vector, parame tric. and symmetric equations of the line containing the point P and paralel to…

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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: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

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Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

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Q: The line that passes through the point (4, -2,0) and parallel to the vector (1, 2, –3) has symmetric…

A: The solution is given in the next step.

Q: Find the distance of point 4(2/3,2) from the line that passes through the origin and parallel to the…

A: follow next step

Q: A vector orthogonal to the plane through the poii (-1,0,0), (0, –2, –2), (2, 3, 4) is < -2, – 10, 9…

A: The given 3 points are A (-1,0,0) , B (0,-2,-2) &amp; C (2,3,4) Let, x1=-1, y1=0, z1=0 x2=0, y2=-2 ,…

Q: 3. Give the parametric and symmetric equations of the line that passes through he point (4, –3, 5)…

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Q: Find two unit vectors orthogonal to a = (-2, 1, 0) and b = (-4,0, 1)

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Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –2, -2), (2,3, 4) is

A: A vector orthogonal to the plane through the points (-1,0,0) , (0,-2,-2) , (2,3,4) is

Q: The cross product of vectors a = (-1, 4, 6) and b = (3, 0, -2) is %3D

A: The cross product of vectors is given below

Q: Give the parametric and symmetric equations of the line that passes through the point (4, –3,5) and…

A: we have to find the equation of line which is passes through the given point and perpendicular to…

Q: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

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Q: Find the general form equation of the plane through the origin and perpendicular to the vector (4,…

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Q: Find the equation of the plane that is parallel to the vectors (3,0,2) and (0,1,2), passing through…

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Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: Find the length of the vector x = [-2, 2, 6 ]

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Q: Provide the parametric and symmetric equations of the line that passes through the point (4, -3, 5)…

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Q: Find both the scalar projection and the vector projection of b onto a, where a = (3, -3, 1) and b =…

A: Consider the given vector: a=3,-3,1b=2,4,-1 Here, the objective is to find the scalar projection and…

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: If a vector is multiplied by a positive scalar, how is the result related to the original vector?…

A: Solution:- If a vector is multiplied by a positive scalar, how is the result related to the original…

Q: A vector orthogonal to the plane through the points (-1,0,0), (0, –1, -2), (2, 3, 4) is

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Q: Write an equation of the plane with normal vector n= (2,8, -4) passing through the point (3,-9,-5)…

A: Vector equation of plane is used.

Q: Find vector and parametric equations of the plane that contains the point P = (-3,1,0) and is…

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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: Give the parametric and symmetric equations of the line that passes through the point (5,−1,3) and…

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Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: A vector is a quantity that has both magnitude and direction. It can be also defined as the…

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

A: The equation of the plane perpendicular to the vector &lt;a, b, c&gt; is: ax+by+cz+d=0 Therefore,…

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…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.