3. The position vector [3 2 1 1] lies in the YZ plane and forms 30 degree with the principal axis. Rotate the object so that it is transformed to ZX plane where it forms 45 degree with the principal axis.

Q: Is the line x = 9- 8t, y= 4 + 2t, z= - 5t parallel to the plane 2x + y-z=2? Give reasons for your…

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Q: Find eguation of a Plane that an contains the vector: and and Z=3E

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Q: 1) in triple dot of vectors |(A x B). C = |(CX A). B\, where the vectors A, B, and C are not same…

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Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non- %3D orthogonal because the dot…

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Q: Find a parametrization of the line through P = (4, 9, 8) perpendicular to the yz-plane.

A: Equation of Linethe Line through P =(x0,y0,z0) in the diresction of vector v→=(a,b,c)is defined…

Q: Find the equation of the plane in xyz-space through the point P=(2,5,5) and perpendicular to the…

A: Given: The point on the plane is P= (2, 5, 5). The plane is perpendicular to the vector n= (1, -4,…

Q: 2. Find the vector, parametric and cartesian equation of a plane that contains the points А(-1,0,…

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Q: Find a vector function that represents the curve of intersection between the paraboloid 2 z = 4x² +…

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Q: Find the equation of a plane that is perpendicular to the vector 3 i - 4j+ 5k and passing through…

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Q: Let M be a plane with the following properties: • M contains the point with coordinates (0,0,1) • M…

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Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

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Q: The equation of a plane n ·〈x, y,z〉= d is said to be in normal form if n is a unit vector. Show that…

A: Given :           The equation of a plane n . <x, y, z> = d is said to be in normal form if n…

Q: The vector (3, -1, 2) is parallel to the plane 6x – 2y + 4z = 1. - %3D

A: Use formula to calculate equation of 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: 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

Q: The vector a in 3-space of length 3 lying in the yz-plane pointing upward at an angle of 5π/6…

A: let w= aiÌ‚ + bjÌ‚ + ckÌ‚   |w|= a2 + b2 + c2 = 1   W is lying in YZ plane and at an angle of 5π/6…

Q: Find the vector equation for the line of intersection of the planes 3x−2y+2z=1 and 3x+4z=−4

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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: Draw a sketch of the plane of 4x – 4y + 2z – 9 = 0. -

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Q: Let M be a plane that contains the point with coordinates (-2,-2,-1) and is orthogonal to the vector…

A: Let M be a plane that contains the point with coordinates -2, -2, -1 and is orthogonal to the vector…

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

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: Find the vector equation for the line of intersection of the planes 2x – 2y – 5z = 5 and 2a + 2z = 1

A: Given  equation of planes 2x-2y-5z=5 2x+2z=1

Q: Consider the plane that goes through the point (4, 1, 3) and is orthogonal to vector (2, 3, 1).…

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Q: A normal vector for the plane 4x −2y + 7z−11 = 0 is ______.

A: We have given equation of plane  4x-2y+7z-11=0 Then, we  can write this as…

Q: Show that the point 1, - 2, 0 lies on both planes 3x-2y+z=7 and x-4y-2z=9. Hence, find the vector…

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Q: Let M be a plane with the following properties: • M contains the point with coordinates (1,1,-1) ()…

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Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane - 6x + 8y – 10z - 4 = 0 are in…

A: We find out the results by using vectors in 3D

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: Let M be a plane with the following properties: • M contains the point with coordinates (-1,1,0) • M…

A: Solution      Plane M contains the point -1,1,0      M is orthogonal to vector 200…

Q: Find an equation of the plane through the origin that is parallel to the plane 4x – 3y + 5z + 10 =…

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Q: Find a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

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Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x² + y²…

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Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

A: Due to our answering guidelines we can only answer one question at a time, therefore I will be…

Q: 1) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

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Q: Let M be a plane with the following properties: • M contains the point with coordinates (-1,-1,0) •…

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Q: The equation ax + by + cz = 0 represents a plane through the origin in R3. Show that the vector n2 =…

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Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

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: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

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: 1 Which vector is perpendicular to the plane -2x + 3y – 4z = 9? 1 1 2' 3 О 2, -3,4] 2 1 9 3? О 12,3,…

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Q: Find the equation of the plane in xyz-space through the point P = (5, 4, 3) and perpendicular to the…

A: NOTE: Refresh your page if you can't see any equations. . the normal vector is  . the given point…

Q: A normal vector for the plane 4x – 2y + 7z – 11 = 0 is

A: Solution is given below:

Q: Which of the following vector is perpendicular to the plane 2x - 3y + 5z +7 = 0? O1-6, 1, 3] O [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: Find a unit vector in the xy plane that is orthogonal 2 to 4 6

A: We have to find the unit vector.

Q: 5) Determine whether the plane 3x – 4y + 5z = 0 and the plane – 6x + 8y – 10z 4 = 0 are in…

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