Let A be the point with coordinates (1, 0, -1) and let B be the point with coordinates (0, 0, -1). Let v be the vector represented by the bound vector AB. Let II be a plane with the following properties: • II contains the point with coordinates (-2,-2,-2) • II is orthogonal to the vector v. What is the distance of the point with coordinates (-2, 1, 2) from II?

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

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

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Q: Find a vector that is orthogonal to the plane containing the points. (Orthogonal means…

A: Given points are, P=3,0,1Q=4,-2,1R=5,3,-1 The orthogonal vector n^ will be calculated from the given…

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Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane

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

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

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Q: Let A(x,y,,z) and B(x,,y2; z,) be two known 3D points. The point M on the line AB divides the vector…

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Q: 7) Find a vector that is orthogonal to the plane that contains the points P(1,–2,4), Q(-2,3,2), and…

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P=(2,0,-4),…

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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, in component form, that is orthogonal to the plane containing the points P = (4,…

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Q: Let v =5j and let u be a vector with length 3 that starts at the origin and rotates in the xy-plane.…

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Q: (a) Show that the point P(5,0,0) lies in the plane r + 2y + 6z = 5 and the point Q(1, –2, 4) does…

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Q: Consider the points below. Р(0, - 2, 0), Q(5, 1, -2), R(6, 3, 1) (a) Find a nonzero vector…

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Q: 9. Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R…

A: Since there is multiple questions, we will solve the first question. Repost the question again and…

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Q: find the vector equation of a plane that contains the intersection line of x + y + z = 1 and x – y +…

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Q: Find nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

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,…

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Q: If a plane is parallel to one of the coordinate planes, then its normal vector is parallel to one of…

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Q: Suppose the light source is placed directly above the xy-plane, so the light rays come in parallel…

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Q: Find two vectors in opposite directions that are orthogonal to the vector        u = ⟨3, 1, −2⟩

A: u=3, 1, -2 Let v=a, b, c be the vector orthogonal to the vector u=3, 1, -2. Then, u·v=0…

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Q: Let vectors u=[1,0,-1] and v=[-2,1,2].Find the vector w that is orthogonal to both u and v

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A: To discuss the linear independence (or otherwise) of the given vectors and describe their span

Q: Let b = 4i + 3j and c be two %3D vectors perpendicular to each other in the xy-plane. All vectors in…

A: Given: b→=4i+3j and c→ are two vectors perpendicular to each other in xy-plane.  To find: All the…

Q: Find a vector that is orthogonal to the plane containing the points P = (3,0, 1), Q = (4, –2, 1) and…

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( – 1,…

A: find the explanation below

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A: Given that U=u1,u2,u3 and V=v1,v2,v3 are two orthogonal unit vectors. Find the equation of vector…

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

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Q: Let b = 4i + 3j and c be two vectors perpendicular to each other in the xy-plane. All vectors in the…

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Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector