(a) Find a nonzero vector orthogonal to the plane through the points P(0,- 2, 0), Q(4, 1, – 2), and R(5, 3, 1). (b) Find the area of triangle PQR.

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: 2. (a) Calculate the position vector for P₁ and the displacement vector from P₁ to P₂, where P₁:…

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Q: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

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 a vector parametrization of the line through P = (3, –8, 5) in the direction v = (-2, 0, 3)…

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Q: Determine the constant a so that the vector i = (2x + 3y)î + (2y – 2z)j+ (x + 2az)k is a solenoidal.

A: Given : The vector v→ = (2x + 3y) i^ + (2y - 2z) j^ + (x + 2az) k^.   To determine the constant a so…

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x= 2+3t y…

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Q: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

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Q: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

A: Find a vector of magnitude 2 parallel to the line of intersection of the planes x + 2y + z - 1 = 0…

Q: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1, √5). Find the coordinates of the vector QS…

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Q: Given a vector A = 3a, - 2a, - 16a, find its components normal to the plane 2x + 2y – z + 8 = 0 and…

A: We have to determine component normal to the plane

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

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

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Q: Find a vector normal to the plane with the given equation. 2x + 8y + 9z = 3 n =

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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: The vector is orthogonal to the plane 4x + 5y –7z =1 Select one: O True O False

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Q: Two vectors of magnitudes A=3 and B=3v2 are lying on the xy plane as shown in the figure. What is…

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Q: What is a vector that is normal to the plane 4x+6(y-100)+7(z-200)=20? O A. 4i+6j-20 k O B. 8i+ 12 j…

A: Given query is to find the normal vector.

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: 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: 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: (c) Find the vector equation of the line of intersection of the planes x-2y+z=0 and x+y=z= 1.

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Q: () 1 (b) Find the length of the component of the projection of the vector a = vector 6 = 2 () onto…

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Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

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Q: 4) a) Find the vector parametric equation of the line in R³ that is perpendicular to the plane 2x -…

A: Given plane is, 2x-3y+7z-4=0

Q: Find parametric equations for the line through the point P(-5,6,7) and perpendicular to the vectors…

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Q: Given the 3-dimensional vectors: A = (xy)i + (2yz)j +(3xz)k B = (yz)i + (2xz)j +(3xy)k Determine the…

A: Here given vectors as A=xyi+2yzj+3xzkB=yzi+2xzj+3xyk

Q: Q5.Find a vector parallel to the line of the intersection of the planes 2x + y – 2z = 5 and. N, = 2î…

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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 the scalar equation for the plane passing through the points P1(2, 1, 5), P2(2, 0, 9), and…

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

A: find the explanation below

Q: b) Find equation of the Plane through point (1, 2, 3) parallel to the vectors V1 = 2i + 3j + k and…

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Q: b) Find out the Vector =y²z?i+x?z?j+z²y²k is irrotational or not?

A: By definition, Any vector is said to be irrotational if the curl of the vector is zero. The given…

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y and…

A: The given curves are: z=4x2+y2     and     x=ey

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: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

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

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