Find a vector that is orthogonal to the plane containing the points. (Orthogonal means perpendicular) P= (3,0,1), Q = (4, –2, 1) and R= (5,3, –1).

Q: Find a unit norm vector that is orthogonal to both the vector (1,2, –1) and the line of intersection…

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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: 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: 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: 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: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

Q: Consider vectors, 2 u = |2, v = w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find…

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Q: Find the unit vector orthogonal to the plane through the points P ( 12, 3, -4 ), Q (-1, -2, 2), and…

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Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

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

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Q: Find the component form of the vector v and (b) sketch the vector with its initial point at the…

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Q: Consider the points P(3, x, -2) and Q(5, 3, 4) in R3 . Find x so that the vector from P to Q is…

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Q: Find the equation of a line in vector form that is parallel to 3x−2y+z= 4, passes through the point…

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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 an equation of the plane that passes through the point P(4, 6, 3) and has the vector n = (1,6,…

A: I have stated the used formula in the solution.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 –…

A: Let's find.

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

A: Given: (2,3,-6) Perpendicular to j vector

Q: Find the value of t such that the vectors v=(2t+1,-3,3t-2) and w=(7,4t+2,2) are orthogonal.

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

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Q: Find a vector equation of the line passing through the points P(-2, 1, 3) and Q(3, 0, -2). 1+t ,te…

A: The vector equation of the line passing through the points A(x1,y1,z1) and B(x2,y2,z2)  is given by;…

Q: M contains the point with coordinates (0,0,1) 2 M is orthogonal to the vector 0

A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

Q: Find the equation of the plane E passing through the point P(2,3,1) and parallel to the vectors K =…

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Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

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: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

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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: 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: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 –…

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

Q: Find an equation of the plane that is parallel to the vectors and , passing through the point (3,…

A: Use given parallel vectors <1,-3,1> , <4,2,0> and passing through the point (3,0,-2)…

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

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Q: га- Find an equation that describes all values of a, b, and c for which the vector w = |b| is NOT a…

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Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

A: Given: X(1, -2, 1) and Y(0, 3, -2).

Q: Find a vector perpendicular to the graph of z = - 3 x2 + 9 y2 – 7 x y at the point (8, 2, -268).

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Q: For which value of k the two vectors u=(3,3,k) and v= (-4,8,1) are orthogonal? *

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Q: Find the vector equation of the line that is perpindicular to the line q(t) = (1,2, 3) + s(2, –1, 1)…

A: Consider a point P(1+2s, 2-s, 3+s) on the vector equation of the line. The vector joining points P…

Q: The plane that contains the point (3, –1, –4) and the line with equation = y – 1 = 3z is orthogonal…

A: Let:x-02=y-11=z-013=kL: x=2k, y=k+1,  z=k3P1:(3, -1, -4)Put k=0, k=1P2: (0, 1, 0)P3: (2, 2,…

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

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Q: Let / be the line through the point with coordinates (1,0,0) in the direction of the vector -2 .…

A: Please rate and feel free to ask any query about any part of the question.  Thanks

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 vector joining the points P1= (-3, 1) and P2= (5, 2) %3D %3D in terms of i and j.

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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 a vector equation of the line r through D4 and perpendicular to the line s through F4 and B1.…

A: Given,D4→ = 1i ^ + 2j^ + 3k^Equation of line passing through D4→ is:x-1a= y-2b=z-3cThe above line is…

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

A: The plane is perpendicular to the given vector 8,3,2. So the direction ratio of the normal vector to…

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

A: Topic = Vector