Determine the general equation of the plane that passes through the point P (-1,1,0) and that has a normal vector n = (2,0, -4).

Q: Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: Find an equation of the plane. The plane through the point (1, 7, 2) and with normal vector 4i + j –…

A: Given:   Point : ( 1 , 7 , 2)  Normal vector : 4i + j - k

Q: The plane with normal vector (0, – 2, – 4) containing the point (-7,4,-3) has equation Aæ + By + Cz…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the linear equation of the plane through the point (6,−2,5) and with normal vector j+2k.

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Q: Find the equation of a plane that is perpendicular to the vector – i+ 2j+ 2k and passing through the…

A:

Q: Find an equation of the plane that passes through the point (1, 3, −7) and is perpendicular to the…

A: Direction ratio of the line n=j is (0,1,0)  Given that the line is perpendicular to the plane.  So…

Q: Write the vector equation for the line of intersection between the planes π1:x−z=−5 and π2:x−y=−1.

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

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Q: Find a vector ū that is parallel to the yz-plane and perpendicular to the vector i = (0, 2, 2).

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Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

A:

Q: Consider the vectors a = (-1,–2, 3), b = (3,0, –2), v = (2, –5, –4) and the plane P given by 2x + y…

A: The given vector is; a→=-1,-2,3b→=3,0,-2v→=⟨2,-5,-4⟩and Plane P is;2x+y=z+13⇒2x+y-z=13…

Q: Verify that it’s possible for a line with direction vector   d=(2,1,-2) to lie flat on a plane with…

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Q: Find the direction vector of the line which is the intersection of the planes x + y + z = 1 and…

A: I am attaching image so that you understand each and every step.

Q: Find the equation of a plane that is perpendicular to the vector 3 i - 4j+ 5k and passing through…

A:

Q: The plane contains the origin and is normal to the vector<4, −1, 5>.

A: Given: (4, −1, 5

Q: Find the equation of a plane that is perpendicular to the vector i+ 2j+5 k and passing through the…

A:

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: 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: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

A:

Q: snip1

A: we have to find the normal and general forms of the equation of the plane that contains the point…

Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: Find the vector equation for the line of intersection of the planes 5x + 2y – 5z = 2 and 5x + 4z = 4…

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Q: Find the equation of the plane going through the point P(2, 3, −1) with a normal vector given by n…

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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 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: 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: A normal vector for the plane 4x −2y + 7z−11 = 0 is ______.

A: We have given equation of plane  4x-2y+7z-11=0 Then, we  can write this as…

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…

A:

Q: Find an equation of the plane that passes through the point (3, 2, 2) and is perpendicular to the…

A: equation of the plane passing through the points (3, 2, 2)               A(x-3)+B(y-2)+C(z-2) = 0…

Q: Write an equation of the plane with normal vector n (7,5, −4) passing through the point (1, −5, 1)…

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Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

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

A:

Q: A normal vector for the plane 4x – 2y + 7z – 11 = 0 is

A: Solution is given below:

Q: Find the linear equation of the plane through the point(1,2,3) and contains the line represented by…

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Q: Find an equation of the plane with normal vector n =, and contains the line given by the y – 2 z - 6…

A:

Q: Determine an equation (in variables x, y, z) for the plane through the point (8, 1, 4), and with…

A: GIVEN- EQUATION OF PLANE PASSING THROUGH THE POINT (8,1,4) AND WITH VECTOR (-2,6,-2) TO FIND-…

Q: Find an equation of the plane that passes through the point P and has the vector n as a normal. ■ 3.…

A: An equation of the plane that passes through the point P and has the vector n as a normal3.…

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 for the line of intersection of the planes 4x + 2y + 2z -1 and 4x + z= -2…

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Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

A:

Q: Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2,…

A: we know that equation of plane which passes through point x1,y1,z1 and normal to vector a,b,c is…

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 <a, b, c> is: ax+by+cz+d=0 Therefore,…

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.