In Exercises 1-8, write the equation of the plane with normal vector npassing through the given point in the scalar form ax + by + cz = d.2. n=(-1,2,1), (3,1,9)

Q: Write down the equations of any two distinct planes with normal vector n = 〈3, 2, 1〉that do not pass…

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Q: To compute h, (x) =*,+0,x,+0,*, in vectorized form then: (theta vector size is 1x3 and X is 3x1) (A)…

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Q: 7. Find an initial point P of a nonzero vector u = PQ with ter- minal point Q(3, 0, –5) and such…

A: We have to find an initial point P of a non zero vector u = PQ→,  with terminal point Q(3, 0, -5)…

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: In Exercises 13-16, find a vector normal to the plane with the given equation.15. 3(x - 4) - 8(y -…

A: Given: The equation of the plane is: 3 (x-4)-8 (y-1)+11 z=0 We have to find the vector normal to the…

Q: A normal vector for the plane through the points (2, 5, 1),(3, 7, 0), and (2, 5, 2) is _____ .

A: Given ,            (2,5,1) , (3,7,0), and (2,5,2)

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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Q: A normal vector for the plane through the points (2, 5, 1), (3,7,0), and (2, 5, 2) is: O (-2, –1,0)…

A: Let the given points in the plane be A(2, 5, 1), B(3, 7, 0), C(2, 5, 2)

Q: Find an equation of the plane that passes through the point P(-8, –3, 7) and has the vector n = (-8,…

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Q: In Exercises 55–60, compute the angle between the two planes, de- fined as the angle 0 (between 0…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find an equation of the plane. the plane through the point (5, 6, 5) and with normal vector 6i + 8j…

A: As we know that the equation of the plane which is passing through a point Px0,y0,z0  and normal…

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

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Q: Find a scalar equation of the plane that contains the points (−1, −3, 1), (1, 0, 3), and (2, 7, 0).

A: We are going to solve

Q: (9) Show that the space curve given by the vector equation r(t) = passes through the point (1, 4,0)…

A: Explained below

Q: Find an equation of the plane. The plane through the point (8, 7, 1) and with normal vector 7i + j -…

A: The equation of the plane is given as:

Q: Find an equation of the plane through the point (4, 5, 1) and with normal vector 6i + j - k. Show…

A: The plane passing through a point A(a) with the normal vector n is given by: r·n=a·n where,…

Q: snip1

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

Q: Give an equation of the plane with a normal vector n = ⟨1, 1, 1⟩ that passes through the point (1,…

A: we know that equation of plane with a normal vector x0,y0,z0 and passes through point x1,y1,z1 is…

Q: What will happen if the Gram–Schmidt process is applied to a set of linearly dependent vectors {v1,…

A: Introduction: The Gram–Schmidt system is a way for orthonormalizing a fixed of vectors in an…

Q: 8.) find a vector of norm 2 that is orthogonal to the three vectors, u=(2,1,0), v=(-1,- 1,0) and…

A: Just assume a vector and apply criteria of perpendicular of two vectors ..as I have done solution in…

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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Q: Decompose the vector ¯b = ⟨1, 0, 4⟩ into its projection proja¯(¯b) and its orthogonal component…

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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: Find an equation of the plane that passes through the point P(-5, –8,8) and has the vector n = (-8,…

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Q: 2- Concisely describe what the following terms mean for a set of vectors and how we quickly check…

A: Define: 1. Collinear vectors 2. Coplanar vectors 3. Linearly independent vectors 4. Linearly…

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

A: Given; n=<7,-5,4> Point (1,-5,1).

Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

Q: What will happen if the Gram–Schmidt process is applied to a set of vectors {v1, v2, v3}, where v1…

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

A: I have append the formula in solution part

Q: Find an equation of the plane that passes through the point Po(0,2, – 2) with a normal vector n =…

A: Find an equation of the plane that passes through the point p0 (0,2,-2)with a normal vector…

Q: A normal vector for the plane through the points (2, 5, 1), (3, 7, 0), and (2, 5, 2) is <

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Q: Find an equation of the plane containing the point P(2,1, –1) and having the normal vector N = -î+3…

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Q: In Exercises 1-8, write the equation of the plane with normal vector npassing through the given…

A: Given  n = i-k, (4,2,-8)

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: Prove that a(-3,2) and b (2,-3) form basis vectors in xy plane

A: a set is said to be basis if set is linearly independent and it spans the space.

Q: In Exercises 1-8, write the equation of the plane with normal vector npassing through the given…

A: Given,  n = k, ( 6, 7, 2) To find  the equation of the plane with normal vector npassing through the…

Q: 6.) Find a vector equivalent to the vector PQ with its initial point at the origin. = (;-2), Q =…

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Q: Let P be the plane through (1, 2, 3), (4, 3, 3), and (4, 4, 1). Find the vector of length 2 that is…

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

A: Given: The maps [0, 1] x [0, 1] to the parallelogram in the XY-plane spanned by the vectors (2, 3)…

Q: Compute the projection of →a→ onto →b→ and the vector component of →a→ orthogonal to →b→. Let…

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Q: 4. Find an equation for the plane through (1, 3, 4), with normal vector .

A: topic- equation of plane with point and normal vector

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

A:

Q: Write the scalar equation of the plane with normal vector * - [3, 4, – 1] and passing through the…

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Q: In Exercises 1-8, write the equation of the plane with normal vector npassing through the given…

A: Our Aim is to write the equation of the plane with normal vector n⇀=(-1,2,1) passing through the…

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

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Q: 1.23. Express the unit vector directed toward the point (x, Y, z) from an arbitrary point in the…

A: Express the unit vector directed toward the point (x, y, z) from an arbitrary point in the plane y =…

Q: a) Find the normal vector to the plane that passes through the points (5, 7, 0), (7, 3, 4) and (1,…

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

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Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

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.