Consider the following. u 3 (-4, =(-4, 6), v = (1, 1) (a) Calculate projy u.

Q: prove thats. u.w V.W V.

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Q: Find inner product of u, v and || u || if u = (1,2,5) and v = (2, –3,5). (Ctrl) -

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Q: Calculate F . dr, where C is the square of (1,1, 1), (–1,1, 1), (-1,–1,1) and (1,–1,1), with…

A: Let F→x,y,z=zex-yezi→+2cosy-xezj→+ex-xyezk→ and C is the square with vertices…

Q: vdor (2,1,3) be the {1,)1), (1, 2, >).(O, 1, 0)1 be the {ll,),l), (1, 2,3).CO,1, 0)) linear…

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Q: orthogonal

A: We have   u=111    and v=2-12 are two column matrices  . We have to find the value of  k so that…

Q: Express the following: as a linear combination of u = (2, 1, 4), v = (1, -1, 6) and w = (2, 2, 8).…

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

A: Let's find non zero unit vector.

Q: Find the component of u along v. u - (-2, 4), v- (1//7, 1/v2)

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Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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Q: 25. Show that |v|u + Ju|v and |v|u – |u| v are orthogonal.

A: Two vectors are orthogonal if their dot product is zero. If the dot product of two vectors is zero,…

Q: Find an upper triangular U (not diagonal) with U2 = I which gives U = u- 1.

A: Given, U2=I

Q: Verify that det A = det B + det C, where Uj + vj U2 + v2 Uz + V3 A = A22 аз1 A32 --EE-E: A12 A22 V2…

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Q: 3 Rnd the lineasion of the hunctran f(xLcos line asiz l

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Q: Show that (u×v)· w = u ·(v×w).

A: As we know that, Multiplication is an Associative Property, i.e. (a x b).c=a.(b x c) and Sometimes…

Q: Consider the vector v between (-5,5, –3) and (1,1, 1).

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Q: 18. Show that u = [2.-5.15] is orthogonal to v = [20,–1,–3).

A: From the given problem:   u→=2,-5,15 ; v→=20,-1,-3   As we know that two vectors u→ & v→ are…

Q: A vector s has initial point (3, 4) and terminal point (5, -1). Write s in the form s = ai+bj. j

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Q: Find the best approximation to u = (3,-7, 2, 3) as a linear combination = (2,-1,-3. 1) and =…

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Q: { (0,0,0), (3,5,6)} is linearly dependent in R' ulgn O ihi O

A: A set containing the zero vector (0,0,0) is linearly dependent.  Therefore the given set {(0,0,0),…

Q: Which of the following vectors is coplanar to [1, 1, 1] and 2, 3]?

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Q: Prove that llu + v|| = llu - vll if and only if u and v are orthogonal.

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Q: 1 Compute the orthogonal projection of v = onto the line L through -6 and the origin. 2 projz (7) 2.

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Q: { (0,0,0), (3,5,6)} is linearly dependent in R ulgn O ihi O

A: Solve the following

Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

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Q: Consider the vector v between (-5, 5, –3) and (1, 1, 1).

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Q: Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3,…

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Q: 2 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

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Q: 4. If possible, express t as a linear combination of u, v, and w. t = (2, 13, 5), = (1,2, 1), v = (-…

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Q: compute the component of u along v. u = (3, 0, 9), v = (1, 2, 2)

A: the given vectors are: u=3,0,9v=1,2,2 we have to compute the component of u along v.

Q: 4 Compute the orthogonal projection of u= 3 onto the line L through and the origin. projz (5) =

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Q: Repeat Exercise 27 for the forces KX = (2, – 3) and KY = (- 2, 3).

A: The given two force vectors are, KX→=2,-3KY→=-2,3 When we find the addition of two vectors, then the…

Q: {(0,0,0), (3,5,6) ) is linearly dependent in R ulgn O İhi O

A: Given {(0,0,0),(3,5,6)}

Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: uz = 1, u2 Uz = u4 u7 -7 , us Compute projs u2, where s = span{u3, U4}.

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Q: 2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

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Q: 10. Show that 1/x, x are linearly independent on (0, 0).

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Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: if u=(1,0,0) and v=(0,1,0), u and v are orthogonal Select one: True False

A: If dot product of two vector is zero then vectors are orthogonal

Q: Show that u and v are orthogonal if and only if ||u + v||² = ||u||2 + ||v||². (Please avoid an…

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Q: If x = v'u and y = 2uv, show that JJ' - 1, where J is the jacobian of u,v with respect to x and y…

A: We have find the jacobian

Q: Suppose u, VE Vand ||u|| < 1 and ||v|| < 1 . Prove it: V1- ||u||?/1- ||u||2 <1- (u, v)|

A: Suppose u, v∈V and u≤1 and v≤1 We have to prove that 1-u21-v2≤1-u,v Here, we have  u≤1 and v≤1 Also,…

Q: Find the stable vector of P = 2 2 2 3 -|3

A: Let stable vector is w= [x  y  z ] So, So, equations to solve

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (−1, −1, 1), v = (−1, 1, −1)

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

A: We have to find a non-zero vector V that is orthogonal to u1=1,2,1 and u2=2,5,4 in R3.

Q: Prove that u, v, w ∈ R3     and [ u x v, v x w, w x u] = [ u, v, w]2

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Q: Find w such that 2u + v u 3w = 0. (0, 2, 7, 5), v = (-8, 4, -3, 1) 1 -- (-) W = 3 -

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Q: on vectors for t2 0.

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Q: u + 1, U2 + V2 1), (a) Compute u + vand ku for u = Solution: Ia + In) (1,2), v = (- 1,:

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 4) Show that, in general, (A.B)" = B".AT How is (A.B) related to (B.A) when both tensors A and B are…

A: 4.

Q: 4. Show that u and v are orthogonal if and only if ||u + v||2 = ||u||2 + ||v||2. (Please avoid an…

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