Consider the bases B- (u, u,) and B' = (u', u'2) for R?, where 8. !3! 8 Compute the coordinate vector [wg, where w = and use Formula (12)( [v]B = P [v]B ) to compute (w. B-B (w]B ? Edit (w]B Edit

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

A:

Q: 2 Let L be the line in R³ that consists of all scalar multiples of the vector . Find the orthogonal…

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Q: Why are there no vectors u and v in R,, such that ||u.||= 2, ||v|| = 3, and    uxv= -7?

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Q: of the vector PP2• -ppositely direct to PP2 and whose norm is the doubl he same direction as PP.…

A: Consider the given point as, P11,-2,1 and P2-1,3,0

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&V…

Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

Q: Consider the Vector-Valued Funcbion く os6) +ド いnct), Cosit)+4 5inct,-20 Ginco since) 015 a Compute…

A: We are given with vector r ;

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

Q: 2 3 Let u and v %3D . Find the length of 2u and the length of -v. - Find the distance between u and…

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Q: Find a non zero unit vecor î that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: The given vectors are u1=(1,2,1) and u2=(2,5,4) in R3

Q: - Given the vector fields Å = yz az – 3x a, +x²y a, B = 3 a, – 4xy a, +y² az Petermine a unit vector…

A: Given that: A→=yzax-3xay+x2yazB→=3ax-4xyay+y2az

Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: Find a vector of length 2 orthogonal to the plane 3x – 4z = 5. %3D

A: Here we have to find the vector of length =2 and  orthogonal to the plane 3x - 4z = 5 Let the vector…

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

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Q: Find the vector in R° from point A = (x, y, z) to B = (-2, –4, 1).

A: Given points  A  = (x,y,z) B = ( -2,-4,1) To determine the vector in R3 from point A to point B

Q: -x + 6y + 2z = 6 1. -x + 3y + z = 7 2 Find the normal vector, n,, to -x + 6y + 2z = 6. n = 1 Find…

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Q: Find a non zero unit vecor û that is orthogonal to u1= (1,2,1) and Uz= (2,5,4) in R³.

A: Cross product of two vector is perpendicular to both vectors.

Q: Show that the vectors 3 do not span R° by giving a vector not in their span.

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Q: Let u be a vector of length 3 in the direction of the positive y-axis and let v be a vector of…

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Q: 19 - By using the definition of the dot product, which vector is orthogonal (perpendicular) to å =…

A: Dot product of two vectors

Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

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Q: 10) (6 points) Using the inner product (v, w) = 3v¡W1+5v2W2 with the vector space R?. a) Find a…

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Q: Let L be the line in R that consists of all scalar multiples of the vector 2 Find the orthogonal…

A: Concept:

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

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Q: Prove: For nonzero vectors ū,vER, if (dot product) ū-v=0, then ū & v are linearly independent. Hint:…

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Q: Find the unit vectoru in the di rection of the vector v=4 (2, 1, 2). 1 u = u = В. 1 12 u = 1 u = 15…

A: v=4(2,1,2)v=(4*2,4*1,4*2)v=(8,4,8)Magnitude of vector|v|=(8)2+(4)2+(8)2=64+16+64=144=12unit vector u…

Q: Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1)…

A: The line integral ∫CF·dr involves the integration over a specific path. In this problem, the…

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A: Given: Aij is a covariant tensor of 2ndorder To find: AijBiCj is an invariant tensor

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Q: 2. Can three vectors in the xy plane R2, have u v < 0, v w < 0, w u<0?

A: Given that, u, v and w are vectors in XY plane. The dot product of vectors is defined as, if u = a1…

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A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: Q3. Prove that (only one): ax-V3ay a- is a unit vector? b- A = 6ax – 3a, + 2a, and B = 3ax + 2a,y –…

A: Given two statements . We need to prove only one out of that  So, here we will prove first statement…

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A: The property used here are b2=b·b x·y=y·x cx·y=cx·y=x·cy Consider the left hand side of the given…

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Q: Find the Duf of f(x, y,z) = z In(x+ y) + e3y on the vector u = 3i -j-4k at Po(1,0,1)

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Q: 4. A unit vector orthogonal to A and whose representations are parallel to the yz-plane.

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Q: 1. Compute the angle Pair Of vectors in Standard inner producy on Mzz. between tre following Mzz…

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Q: 3. Show (using the concept of vectors) that the area of the triangular region with vectors u 1 and v…

A: Given that, The vectors u and v are the vectors of the adjacent sides of the triangular region.…

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: ind a vector orthogonal to both u and j+k. u=2i-j+3k

A: we have been given two vectors,  u = j+k. v=2i-j+3k   the unit vector that is orthogonal to both…

Q: 1.23. Express the unit vector directed toward the point (x, Y, z) from an arbitrary point in the…

A: Express the unit vector directed toward the point (x, y, z) from an arbitrary point in the plane y =…

Q: 2. Verify that the usual length of Vector in the has the plane properties in 3 dinensional Space…

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Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero

Q: Find the work done by the force F=(1,3) in moving an object from A(4, 5) to B(-2, 8).

A: Explanation of the answer is as follows

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.