Derive the vector triple product formula a × (b × c) = (a · c)b - (a - b)c. . ↳s a hint for a good start: lª × (b × c)]k = €ijkQi[b × c]j. ) [a

Q: ..... A= -1 1 is diagonalizable. Select one: True False

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Q: Show that

A: Given,  To prove 1  1    1a    b    c  a3      b3     c3=a-b(b-c)c-a(a+b+c)

Q: Use the dot product to determine whether v = 5i and w = -6j are orthogonal.

A: Given:

Q: Let a = 2 (-) (-3). 1 and b = What is a|²|b²+ la · b|²? -2 be two vectors.

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Q: Use the vector w= (20, -15) ||w||-19 ||w||-19=

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Q: 6. is applied to the 6. When the transformation -18 vector v = the resulting vector is 54 Write down…

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Q: Let vector v = 3i – 2j+ 4k and point P = (0,0, -3). For what point Q is it true that v = PQ?

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Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Find the dot product of a = and b = .

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Q: The vector result of (ì − 2j +3k) · (−2ī + 2j − 2k) is a. -i + 7j b. -i+j-k d. j+7k e. -i+7k c.…

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Q: r(t) = (x(t), y(t), z(t)) where x(t) = – 4t2 – 5t – 3 y(t) = 5t² + 5t +3 z(t) = – 5t? - | '(t) =…

A: Here, we need to find the binormal vector B. We are given that r(t)=<x(t), y(t), z(t)> where…

Q: Find the direction cosines of v =〈3, 6, −2〉.

A: Given vector is v=3,6,-2. To find the direction cosines of given vector. Solution: We know that if…

Q: 1. Consider the following vectors: a = 2í +33, 8 = -27+3k, and ở = -37+ 237 Compute the following…

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Q: Find the following dot product. (-19,3) · (16,-6)

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Q: 2. Which polygon is the translation of polygon 1 by: (a) vector AB? (b) vector BC? EN B 3 4 nob C…

A: Given:

Q: Use the dot product to determine whether v = 5i and w = -6i are orthogonal.

A: The given vector is v=5i  and  w=6i known fact: Two vectors a and b are orthogonal (perpendicular)…

Q: For vectors and shown, drawu - 2 13 19 V

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Q: Simplify each vector operation. a) j·(-j) b) (i ×j)·k c) (i ×j)xk

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Q: 4. Show that a 6 a + %3D

A: Here simply open the squre term and then simplify as a.b=b.a

Q: z= 2e'+i

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Q: Find the dot product v • w. v = 6i + 8j, w = – 13i – 8j O A. - 78 А. О В. - 14 О С. -64 O D. - 142

A: Explanation of the answer is as follows

Q: Which of the following statements are true for all vectors a, b? A. ||a - - b||² B. a∙b=0⇒a=0 C. a.…

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Q: Consider each A and B vector, make each of the following below TRUE or FALSE, and give brief…

A: To prove: A+B→ < A→OrA+B→2 < A→2…

Q: Given u⃗ =⟨2,−5⟩ and v⃗ =⟨4,−4⟩, find the dot product u⃗

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