Find an equation of the plane. The plane through the point (6, 1, 5) and with normal vector 5i + j - k

Q: Find an equation of the plane. the plane through the point (9, 2, 5) and with normal vector 3i + 5j…

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Q: Find the equation of a plane that is perpendicular to the vector 4 i + 2 j - 2 k and passing through…

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Q: a) Find equation of the Line through point (2,3,0) perpendicular to the vectors U1 = i+2j+ 3k and U…

A: Line through point (2, 3,0)  Which perpendicular to U1 and U2

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: Find the area of the triangle determined by the points P, Q, and R. Find a unit vector perpendicular…

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Q: Find the equation of the plane that contains the point (4, – 1, 3) and is perpendicular to the…

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

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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 =<1,3>

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

A: A plane is a two dimensional surface which is spanned by two linearly independent vectors.

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

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Q: 4. Find an equation (in point-normal form) of the plane containing the points K, M, and N. 5. Let R…

A: This is a problem of Vector Algebra.

Q: Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

A: Given  The vector equation is  0i +2j+k  The line passing through origin , origin is  ( 0 ,0 ,0)…

Q: 1. A plane is defined by the equation x - 7y - 18z = 0. a. What is a normal vector to this plane? b.…

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Q: Find the parametric form of the equation of the line passing through the point Po(-2,-1,3) and…

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

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Q: 2. A plane is defined by the equation 2x - 5y = 0. a. What is a normal vector to this plane? b.…

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

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Q: Derive a parametric representation and find a normal vector for the plane 6x – 2y + 10z = 16. NOTE:…

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Q: The equation of a plane n ·〈x, y,z〉= d is said to be in normal form if n is a unit vector. Show that…

A: Given :           The equation of a plane n . <x, y, z> = d is said to be in normal form if n…

Q: 6. For a plane with a normal of ñ = [1,2,-9] and containing a point P (3,-4, 0), write the scalar…

A: Given: Normal of the plane π is given by, n→=i→ + 2j→-9k→ Point P on the plane is P3,-4,0 To find…

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

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

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Q: Find equation of Plane that an contains the vector: and 1-6 and Z=36

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Q: Find an equation for the plane through the point P = (-4, 6, -3) which is perpendicular to the…

A: Topic- equation of plane

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

A: Equation of line passing through the point (x1,y1,z1) and is perpendicular to the plane (ai+bj+ck)…

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: Let N = i − j + k. (a) What is the equation of the plane P containing (0, 0, 0) with normal vector…

A: a) The given normal vector N is 1,-1,1. The equation of plane is Ax-x1+By-y1+Cz-z1=0. Substitute the…

Q: E. Find an equation of the plane passing through the point (6, 3, 5) and containing the line of…

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Q: Find an equation of the plane. The plane through the point (3, 2, 3) and with normal vector 9i + j…

A: Consider the provided question,

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: Q8. Find the equation of the plane passes through the point (1,2,3), parallel to the vector…

A: We have to find the equation of a plane passing through a given point and parallel to two vector.…

Q: b) Find parametric equations of the plane (P) containing the point P(1,-2, 0) and the vectors û and…

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Q: ': Find all unit vectors parallel to the and perpendicular to the plane vector V = 5i -j + 2k

A: Here we find all unit vector parallel to the yz plane and perpendicular to the vectorv→=5i∧-j∧+2k∧

Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, −1,…

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

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Q: (a) Find a vector n perpendicular to the plane z = 8x + 9y. (b) Find a vector v parallel to the…

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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: Find the Cartesian equation of the plane containing the points A(1,0,3), B(1,1,-2) and C(-1,2,0).

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Q: Find the equation for the plane through the point Po = (2,7,6) and normal to the vector n= 3i + 5j +…

A: Given:-normal, n=3i+5j+6kpoint on the plane, P0=2, 7, 6let (x, y , z) on the plane vector (x-2)i+…

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 equation of the plane containing P and orthogonal to the line r(t). Write your answer in…

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Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

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Q: 16. Find an equation of the plane through the point (1, 1, –2) and parallel to the plane 3r – z =

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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: 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 the equation for the plane through the point Po = (8,4,8) and normal to the vector n=2i + 2j +…

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