Find a set of vectors {u°, v*} in R4 that spans the solution set of the equations w-x-2y+3z=0 4w+2x+y-2z=0.

Q: find a vector b so that the equation A = b has infinitely many solutions?

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Q: a) Find equation of the Line through point (2,3,0) perpendicular to the vectors U1 = i+2j+ 3k and U…

A: Line through point (2, 3,0)  Which perpendicular to U1 and U2

Q: Decompose v into two vectors, v1 and V2, where v is parallel to w and v2 is orthogonal to w. v=i+j,…

A: A vector parallel to w can be obtained from the following formula, v1=v.ww2w and the other 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 a vector v parallel to the intersection of the planes - (2x + 4y + 3z) = 4 and 3x + y + z = 7.

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 3y+4z=−3 and 5x+y+2z=4

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Q: (d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three…

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 3x−3y−4z=5 and…

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Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: If v and w are two non zero vectors, the vector projection of v onto w is  projwv=v.ww2w Substitute…

Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

Q: snip

A: We know that two vectors u and v are said to be orthogonal if their dot product u . v = 0. Given…

Q: What is equation of the plane passing through the point A(-2, –1, –3) and parallel to the vectors ā…

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Q: Given A = x(2z -y) + ŷ(3x-2z) – 2(x+3y), find a unit vector parallel to A at point P =(-2, 1,–3).…

A: Vector valued functions are the rule that used to fix or associate a vector to a particular point…

Q: Decompose the vector v=3i+2j into two vectors v1 and v2, where v1 is parallel to w=2i+j, and v2 is…

A: Decompose v into two vectors v1 and v2,where v1 is parallel to w and v2 is orthogonal to w.v=3i+2j,…

Q: Find the cartesian equation of the plane that is normal to the vector n = -3i – 4j+4k and includes…

A: n=-3i-4j+4k  and P(2,-7,5)

Q: When decomposing the vector into the sum of two vectors the first is parallel to the other vector…

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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 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 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: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

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Q: Find a set of vectors {u, v} in R* that spans the solution set of the equations w - x -y+ 3z 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: Are the vectors v = 6i - 3j and w = i + 2j orthogonal?

A: Two vectors are considered to be orthogonal if their dot product is zero.

Q: Find the possible values of x if vectors are j +2k, v =2i + j –- k and w = xi+j - k coplanar: u = i…

A: Given vectors are u=i-j+2k, v=2i+j-k and w=xi+j-k. To find the possible values of x if vectors are…

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: Find a non-zero vector x perpendicular to the vectors  v= [-3]    And u = [-1]      [11]…

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Q: Find a vector normal to the plane -2x - 3y = 12 - 4z.

A: Given  a vector -2x-y=12-4z. We need to find the vector normal to the plane.

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: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

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Q: Find a set of vectors {u, v} in Rª that spans the solution set of the equations w – x + 2y – 4z 0,…

A: The detailed solution is given below Thank you

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 v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

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 nonzero vectors u, v, w that are perpendicular to (1, 1, 1, 1) and to each other.

A: Then   -------------(1) Also  --------------------(2)

Q: Find a set of vectors {u, v} in R“ that spans the solution set of the equations 0, 0. w – x – 3z 5w…

A: To find a set of vectors {u,v} in R^4 that spans the solution set of the equations

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: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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Q: Find a set of vectors {u, v} in R* that spans the solution set of the equations w -x-y+ 3z 5w + 2x +…

A: In the question it is asked to write the vector for the given equations. w-x-y-3z=05w+2x+y+3z=0 AS…

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

A: Solution is given below:

Q: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

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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: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

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Q: Find the cross products uxv and vxu for the the vectors u = 3i-j-2k and v=i+2j-3k.

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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: Evaluate /1+ x² + y²dS, where S is the helicoid with vector equation т(и, 0) - = 0 < u < 3, 0 < v <…

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

A: Answer

Q: Find a nonzero vector parallel to the line of intersection of the two planes 5z – (3x+3y) : 2 and 2x…

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