Find a nonzero vector parallel to the line of intersection of the two planes – (2x + 3y + z) = -2 and 5x + y+ 2z = -2.

Q: find the angles between the vectors:x+y=1,2x+y-2z=2

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Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: Find a nonzero vector parallel to the line of intersection of the two planes 2y 5x - 3x = -5 and 5y…

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Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: Find a vector parallel to the line of intersection of the planes 2x + 3y – z =11 and 4x + 2y – 3z =…

A: We need to find a vector parallel to the line of intersection of the planes 2x+3y-z=11 and 4x + 2y -…

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 two vectors v1 and v2 whose sum is ⟨−3,5⟩, where v1 is parallel to ⟨1,−1⟩ while v2 is…

A: Given Data: The sum of vector v1 and v2 is <-3,5>. The vector v1 is parallel to the vector…

Q: The unit vector of the column on the plane 2x + 2z - 4y = 3 is the vector.

A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

Q: Find two linearly independent vectors perpendicular to the vector 1 3

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Q: Find two vectors v1 and v2 whose sum is ⟨−5,0⟩, where v1 is parallel to ⟨5,1⟩ while v2 is…

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Q: Find an equation of the plane passing through (0,-2,3) that is orthogonal to the planes 2x+ 2y-5z 0…

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Q: What is equation of the plane passing through the point A(-2,-1,-3) and paralleto the vectors a=3+2k…

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Q: Find an equation of the plane. The plane through the point (2, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

Q: Find a vector equation for the line through the point Pla,-1,0,3) that is orthogonl t the hyperplane…

A: Suppose a line passing through the fixed point with position vector a and parallel to vector b, then…

Q: Find the vector equation for the line of intersection of the planes 5x + 2y – 5z = 2 and 5x + 4z = 4…

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Q: Find the direction vector of the line of intersection of the planes x + 2y +z = O and x+y+1 = 0. %3D

A: Line of intersection of two planes

Q: Find a vector in component form that is perpendicular to the line 3x 4y = 6.

A: To find the vector in component form that is perpendicular to the given line.

Q: Find a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

Q: Find a vector v parallel to the intersection of the planes - (x + 3y + 4z) = 7 and 2y – 2x + 2z = 7.…

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

Q: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

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Q: s the vector ở = (-1,–2,3) perpendicular to the plane 3x + 6y – 9z + 5 = 0? %3D

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Q: Find a vector v→parallel to the intersection of the planes 3x+y+2z=3 and       −(x+2y+4z)=7

A: Vector parallel to intersection of two planes is cross product of the normal vectors of the two…

Q: For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

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Q: Find an equation of the plane passing through (0,-1,3) that is orthogonal to the planes 3x+4y-2z=0…

A: Let's find equation of the plane.

Q: Express the unit vector directed toward the origin from an arbitrary point on the line described by…

A: solution : Given the point x=0, y=3 and z1.22unit vector is defined…

Q: For which positive value of x are the vectors (-14x, 2, 1), (2, 3.x², –10) orthogonal?

A: Given:- vectors <-14x, 2,1> , <2, 3x2, 10> To find:- positive value of x when both…

Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

Q: Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

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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: 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 the Directional Derivabive of Pary,2)= x-yz'+ at the point CI, -2, 0) in the direcbion of…

A: A scalar function is a rule to associate a number to a particular point in space. The directional…

Q: Find a vector v parallel to the intersection of the planes 3x + y + 2z = 3 and – (x + 2y + 4z) = 7.

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Q: Find an equation of the plane that passes through the point (3, 2, 2) and is perpendicular to the…

A: equation of the plane passing through the points (3, 2, 2)               A(x-3)+B(y-2)+C(z-2) = 0…

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y2 + 2z2 + 4x – 4z = 0.

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Q: Find the equation of the plane in xyz-space through the point P = (4, 2, 4) and perpendicular to the…

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Q: Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1,…

A: Initial point is P0x0, y0, z0 and the terminal point is P1x1, y1, z1.

Q: Find the equation of the plane in xyz space through the point P= (3,3,4)and perpendicular to the…

A: We need to find equation of plane.

Q: Find the vector equation of the plane taking into account that 4x - y - z = 3

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Q: 2) Find the vector from the origin to the center of the sphere 2x² + 2y² + 2z2 + 4x - 4z = 0.

A: The equation of the sphere is, 2x² + 2y² + 2z² + 4x - 4z = 0 So, x² + y² + z² + 2x - 2z = 0 So, (x²…

Q: Determine the scalar equation of the plane that passes through (5, -5, 5) and is perpendicular to…

A: Here we will find the required equation of the plane,

Q: Find the vector of velocity which has a speed of (90m/sec) and parallel to the vector joining the…

A: Let Vector a is parallel to vector b then vector a = K Bn Where K is some constant and Bn is the…

Q: Find a non-zero vector perpendicular to the vectors -2 and ü = 2 ||

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Q: Find the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the…

A: topic - equation of a plane

Q: 2) Find the vector from the origin to the center of the sphere 2x2 + 2y² + 2z2 + 4x – 4z = 0. |

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Q: Find the vector equation for the line of intersection of the planes 4x + 2y + 2z -1 and 4x + z= -2…

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 4x-2y+z=-1 and…

A: Answer

Q: Find a vector that is perpendicular to the graph off (x, y) = 3 + 3x−y at (x, y).

A: Given: fx,y=3+3x-y The normal vector to the given graph can be determined by the gradient of the…

Q: Solve for the linear equation of the plane through the origin and perpendicular to the vector…

A: Topic:- geometry