3-2. Prove the triple scalar product identity А (Вх С) 3 (АХ В): С.

Q: 4. Two uniform vector fields are F = 2a, +3ā, -5ä,. Find ExF. given by E=-3a +5ā, +2㸠and

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Q: 2- We can write the vector x = (19,–1,–) in R³ as a linear %3D combination of the vectors x1 = (4,2,…

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Q: Given that p and r find in column vector form:

A: In this question, we find the column vector by using the given vectors.

Q: What must be value of X so that B is diagonalizable?

A: A matrix A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such…

Q: D. Prove i [- 2,5, 1], 7 = [2,1, – 1] and w [- 6,0, – 12] are orthogonal. %3D

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Q: (a) Prove that if u is orthogonal to both v and w, then u is orthogonal to v + w. (b) Prove that if…

A: Given: (a) If u is orthogonal to both v and w. To prove:  u is orthogonal to v + w. (b) If u is…

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: (-2,3,1,0,2). Find scalars a and b so that аи + bv 3 Let u = (2,1,0,1, –1) and v = (-8,8, 3, – 1,7).

A: u=2, 1, 0, 1, -1  &  v=-2, 3, 1, 0, 2

Q: Let U(7, 6, -5), V(2, 8, -2), and W(1, 10, o). calculate the scalar triple product U.(VxW) Answer:

A: Given that  The vectors U(7,6,-5) V(2,8,-2) and W(1,10,0) To find the U(V*W)

Q: Prove i = [- 2,5, 1], = [2,1, – 1] and w = [-6,0, – 12] are orthogonal. %3D %3D %3D

A: SEE ATTACHMENTS

Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 5u . (3v - 4w)or vector.

A: It is given that  u = -i + j, v = 3i - 2j, and w = -5j

Q: Calculate the scalar triple product u · (v × w), where u =〈1, 1, 0〉, v =〈3, −2, 2〉, and w =〈4, −1,…

A: The vectors are, u=1,1,0v=3,-2,2w=4,-1,2 We need to find the scalar triple product u·v×w

Q: The scalar product 0v is 0.

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Q: The unit vector in 2-space that makes an angle of π/3 with the positive x-axis is _____

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Q: Let u = [-1 3 -1] and v =[-6 0 5]. Find the vector w = 2u – 7v and its additive inverse. %3D

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Q: If Apq is a symmetric tensor, Bpq is an anti-symmetric tensor, then prove that ApqBpq = 0

A: Given two tensors Apq & Bpq such that Apq is symmetric and Bpq is anti-symmetric. To prove that…

Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 4u . (5v - 3w)or vector.

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Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar proju(v + w) or vector.

A: Here given vectors as u = -i + j, v = 3i - 2j, and w = -5j. Thus  v+w=3i-2j+-5jr(say)=3i-7j

Q: Under what circumstance is the scalar projection of u onto v equal to the scalar projection of v…

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Q: Suppose that f is a vector of length 8 with F1{feven} = -2 – i and F{f»dd} = 3+i. %3D Compute the…

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Q: find all the scalars k such that || kv || = 3, Where v = (-1, 2, 0, 3)

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Q: 2. Use abbreviated index notation to prove or disprove the following statements involving arbitrary…

A: Since there are multipart, so here find the solutions of first and second part.

Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'v' where needed to give…

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Q: 6. A student claims to have found a vector A such that (2i - 3j + 4k) x A = (4i + 3j - k). Do you…

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Q: The inner product of anti-symmetric and symmetric tensor is а. 1 b. 0 С. -1 d. none of the above

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Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'V' where needed to give…

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Q: Suppose A = 4i-6j, B = i + 7j, and C = 9i - 5j. Then the scalars h and k such that A = hB+ kC are…

A: Topic = Vector

Q: Suppose A = 4i − 6j, B = i + 7j and C = 9i − 5j. Find (a) scalar projection of A onto B (b)…

A: We know that The scalar projection of A on B is  A.B|B| vector projection of C onto A is A.C|A|2A

Q: Show that V² (v-x) = 2V.v+x-V²v, where v is a vector field and x is the position vector of a point…

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Q: 1. If øis any scalar then V × Vø = 0 is TRUE or SOMETIMES FALSE SOMETIMES CANNOT FALSE TRUE FALSE?…

A: We have to use the cross product to prove the given problem.

Q: Recall that the Euclidean scalar product in R² is defined by (x1, Y1) · (x2, Y2) := X1T2+ Y1Y2 - (i)…

A: Since you have posted multiple questions but according to guidelines, we will solve first question…

Q: If d is a scalar multiple of b, then ax%. Select one: True False

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Q: Given that complex u and v,  prove that: ||u| - |v|| ≤ |u - v |

A: In the given question we have to prove that                     for two complex number u and v…

Q: Use the quotient law for tensors to show that the array -2xy -2xz /y²+z²-x² -2yx x²+z²-y² -2yz -2zx…

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Q: 24- If the vector A = 2i + 4j – 3k in the primed triad i/ j/ k/ in which the x/, y/ axes are rotated…

A: Vectors are the quantities which represent magnitude as well as direction. The unit vector i, j and…

Q: Compute the orthogonal projection of u'onto v. Use the square root symbol 'v' where needed to give…

A: Given vectors are u→=−64−6 and v→=−23−2. We have to find the projv→u→. We know that…

Q: |The vector projection of v = 4î + 4j + 4k onto W = 5î - 4ĵ + 3k is aî + bî +cê: where the exact…

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Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 5v.

A: Given vectors are u=2i-5j, v=-3i+7j and w=-i-6j. To find: The vector or scalar 5v. Solution: When we…

Q: 6. Use the scalar triple product to determine if the points A(1,3, 2), B(3, –1,6), C(5, 2,0), and…

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Q: 9. The triple scalar product is given by (u x v) w = E,",V,W Expand this equation X V and simplify,…

A: Let u=(u1 , u2 , u3 ) and v=(v1 , v2 , v3 ) and solve it.

Q: Denote three scalars A = eTE-le, B = µTE-le and C = µTE-'µ. 1. Prove that AC – B² > 0.

A: We are given three scalers A,B,C in terms of weighted matrix inner-products, and we have to prove…

Q: Let TA : R → R³ be multiplication by the orthogonal matrix 1 21 3 3 3 6- 1 Find TA(x) for the vector…

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Q: 8) Let A be an nxn ma tiX. vector b the equation Ax = b has more than one solution. Explain why A is…

A: Invertible matrices

Q: Suppose cu =0 for some nonzero scalar c. Show that u= 0. Mention the axioms or properties you use.

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Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: proju (v - w)

A: Given that, u = -i + j v = 3i - 2j w = -5j Then we get, v - w = (3i - 2j) - (-5j) = 3i - 2j + 5j =…

Q: Calculate the scalar triple product u· (v x w), where u = (1, 1, 0), v = (2, –3, 5) and w = (4, –1,…

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Q: Find the scalar product of x and y x =(-1, 0, 2) and y =(-7, 7, 3)

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Q: The scalar projection of the vector 7 = (-2, 3, 1) on 7= (2m, -1, 3) is -1. Determine the value of…

A: Follow next step

Q: 5) Find the scalar and vector projections of b onto a. a = 5i – k, b= i + 2j + 3k %3D -

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