A plane intersects the a1, a2 and a3 axes at 0.2, 0.1, and -0.5. The reciprocal vector perpendicular to such plane is a. 5b1+10b2-2b3 b. 50b1+10b2-20b3 c. 50b1+100b2+20b3 d. 5b1-10b2-2b3 e. 50b1+100b2-20b3

Q: Find equations for the planes The plane through A(1, -2, 1) perpendicular to the vector from the…

A: The normal vector of the plane is given by A(1,-2,1)  The point of passing is (0,0,0). The equation…

Q: Find the vector equation of the line of intersection, if it exists, for each pair of planes. a. 2x…

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Q: Consider the points A(1,-5), B(-1,3) and K(4,-2) in 2D. A. Determine the vector AB B. Determine the…

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Q: Find a vector equation for the plane that contains the points P, Q and R Find a scalar equation for…

A: Given points: P(2,1,1),Q(0,4,1),R(−2,1,4) and S(1,5,−4) Equation of a plane in cartesian form…

Q: Given the vectors in parts a) and b), determine whether u, v, and w lie in the same plane when…

A: We have to determine whether vectors u, v and w lie in the same plane when positioned so that their…

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

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Q: Which of the following vectors is perpendicular to the plane 2x - 3y + 5z + 7 = 0?   a. [-3, 2,…

A: Given: The equation of the plane is  2x - 3y + 5z + 7 = 0   To determine: The vector which is…

Q: 35. The position vectors of the points A and B are OA =2i + j- 4k,OB =-2i +4 j – 2k , a vector…

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Q: Which of the following vectors is orthogonal to the plane 3(x - 7) + (y + 8) - 5z = 15? O O O

A: Given equations of plane 3(x-7) +(y+8)-5z=15this is an equation of the form a(x-x1)+b(y-y1)+…

Q: Let r = ri+y1j+z¡k, r2 = 1zi+ Y2j + zzk and r3 = r3i+ yaj + z3k be the position vectors of points…

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

A: We have to find the equation of plane.

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

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Q: What angle does the line of intersection of the planes (x 2y + 3z 5 and 4x+y-2z-7 make with the…

A: The dot product of two vectors u→, v→ is calculated using the formula: u→·v→=u→v→cosθ, where θ is…

Q: 4. Identify the component form of the vector that maps AABC to its image AA'B'C' A. B. 2 C. D.…

A: Given graphs  1) vector that maps  triangle ABC has vertices A(3,-1),B(7,-3),C(1,-6) to its image…

Q: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

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Q: Find a vector parallel to the line of intersection of the planes x+ 3y – 2= =13, and 3x – 4y + = =-8…

A: Solution is here

Q: Use the triple scalar product to find the value of p that makes the three vectors below coplanar.…

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Q: 2. Let each of the vector A = -8a, + 2ay – 4a,, B = 3ax – 4ay |3D Z> + 5a,, and C = 4ax + 5a, extend…

A: Using position vectors of given points. we ca find side vectors of triangle. using magnitude of a…

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

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Q: 2. Given the points P(-1,3, 1), Q(0,5, 2), R(4,3, –1), (a) Find a nonzero vector orthogonal to the…

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Q: Find an equation of the plane that contains the point (-1, 2, 3) and is perpendicular to the line…

A: The plane is perpendicular to the line, then the direction vector of the line is normal to the…

Q: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

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

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Q: 1. Use the vectors in the figure at the right to graph each of the following vectors on the plane…

A: Draw the correct vectors 2v & -3w than form the triangle sum.

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: Consider the vector y = [1 2 3]. Find the orthogonal projection of y onto the plane x, - 2x2 + 4x3 =…

A: Given vector is y=1,2,3 Given plane is x1-2x2+4x3=0 Normal vector to the p[lane is n=1,-2,4…

Q: Given a vector Á = 3a, + 2a, + 6as , determine the vector component of Á perpendicular to the…

A: Topic:- vector

Q: 10. In the diagram, M is the mid-point of CD, BP:PM = 2:1, AB AD = z. = x, and AC = y and %3D…

A: Given that:                               NOTE: As per our answering guidelines, we can only answer…

Q: find the two-dimensional vector equation of the line r(t) = a +t*m such that - r(0) has norm 8 and…

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Q: Q1:A-Find the equation of plane passes through (0,2,-1) parallel to the plane 3x+y+z=7? b- Find…

A: 1. A. According to question,Given plane,3x+y+z=7,Given Point 0, 2, -1

Q: 4. Identify the component form of the vector that maps AABC to its image AA'B'C' A . 2 B. C. 2 A4…

A: Observe the given figure to identify the coordinates of both A, B, C and A', B', C'. x coordinate…

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

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Q: )P=(3,2,1), then the parametric equation of the line is :   a.

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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

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

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Q: 4. Identify the component form of the vector that maps AABC to its image AA'B'C A. B. C. D. ぐ 21…

A: first we write thev coordinate of the vertex of each trangle

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: Find the vector and the cartesian equations of the plane containing the point î+ 2j – k and parallel…

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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 an equation of the plane passing through the given point and perpendicular to the given vector.…

A: Equation of a plane perpendicular to a, b, c and passing through x0, y0, z0 is, ax-x0+by-y0+cz-z0=0

Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), 0(2, 0, – 1), and…

A: It is given that the plane contains  P(1,0,0), Q(2,0,-1) and R(1,4,3). Let, Equation of plane…

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.