3. Let U-= 4 And v = -1 -3 be two vectors in R3. (A) Calkülateu x v. (b) Determine an equation in normal form for the plane Il passing through the origin and which is tensioned by 20 and 3v. v. (<) Determine AN orthogonal base for R3 that contains tWD vectors that lie i planet II.

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: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

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Q: What are the components of vector p which has three times the magnitude of the normal vector of the…

A: Given plane: Let the normal vector be n. So,

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Q: find a vector parametrization for the line with thegiven description.Passes through P = (1, 2, −8),…

A: Find a vector parametrization for the line with the given description. Passes through P = (1, 2,…

Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=&lt;  ,  , 0…

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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: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: 3. Two lines in the plane are perpendicular when the product of their slopes is -1. Apply this to…

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Q: Find a unit vector in the xy-plane that is orthogonal to

A: Here given vector as a=123 Consider a vector as b=25-150 Now find the dot product of vector b to…

Q: find a vector parametrization for the line with thegiven description. Passes through O and (4, 1, 1)

A: To findvector parametrization passes through O and (4,1,1)

Q: 10) Eind the eçuation of the plane Contaihins the two vectors 2and ,and the point PU2ー)

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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 an equation of the plane. The plane through the point (8, 7, 1) and with normal vector 7i + j -…

A: The equation of the plane is given as:

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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

Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

Q: 3) Write down the equation of line in a vector parametric form, scalar parametric form and standard…

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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: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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

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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: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

A: The scalar equation of the plane with normal vector [4, -1, 9] and passing through the point (2, -1,…

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: 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…

A:

Q: 8. Consider the following two planes: one with equation 4x – 5y + z = -2, and the other which passes…

A: Given: Given, equation of the plane, 4x- 5y +Z = -2 The other plane passing through the point (1, 1,…

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

A:

Q: Find an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

Q: 5. Verify that its possible for a line with direction vector J=(2,1,-2) to lie flat on a plane with…

A: The vector equation of a plane is given by the expression . Here, and are the vectors that lie on…

Q: Determine any three points on the plane given by 5x - 6y + 10z - 15  = 0. Using these points, give a…

A: The given plane is: 5x - 6y + 10z - 15  = 0. We have to find any three points on the plane. Using…

Q: Find an equation of the plane. The plane through the point (4, 8, 6) and with normal vector 7i + j -…

A: Given, The plane passing through the point (4,8,6) with the normal vector 7i+j-k We know that, The…

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

A: Solution is given below:

Q: generate a parametrization of the line through P(2, -4, 7) parallel to v1 = 2i - j + 3k. Then…

A: We know that equation of line through (x1,y1,z1)  and parallel to ai+bj+ck is

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 Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

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Q: Find the linear equation of the plane through the point (2, −2, 6) and with normal vector j+2k.

A: Explanation of the solution is given below...

Q: Write the equation of the plane with normal vector n = (1, 3, 4) passing through the point (3, -1,…

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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: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

A:

Q: 9. Find both vectors of length 5 that are perpendicular to plane 2x + 2y +z - 4 = 0.

A: Explained below

Q: -2 - are the vectors U, = %3D Ug = %3D in M22 are lineor ly depon dent linearly in dependet.

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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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