Let a, b, c and ij be the three dimensional vectors ä=j+5k, b=-27+6j+8k, č=57+8j, j =-67+3j Perform the following operations on these vectors: (a) ca+äÿ (b)(a b) a (c) ((cc) a) a

Q: Determine the dot products of the following pairs of vectors. (a) (3, 5), (3, -4) (b) (2, -5, 3),…

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Q: Determine nonzero vectors that are orthogonal to the following vectors. (a) (1, 5)     (b) (6, −1)…

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Q: Specify the unit vectors a = 2i + 3j-k and b = 3i + 4j.

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Q: Consider the vectors: å = ỉ– 3j + 2k , b' = 4j – 2k and ở = i + k in 3D A. Write 3a – 4 b - 2¢ in a…

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Q: Find a vector, w, which is perpendicular to the vectors where u = 101-20 +14k and v=-20 +10ĵ-5k W +…

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Q: a.A = 6-j8, B=8-j6 bA=6+j8, B=8-j6 c. A = 6-j8, B=-8+j6 C.

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Q: What is the resultant of vectors a and b? ( A ) GL B

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Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

Q: Find the angle between the vectors u = (-3,1,–2) and v = (-7,-5, 2) %3D

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Q: Find the value of a so that the vectors a = (11, −29, 13), b = (46, 5, 37), and c = (a, -194,-70)…

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Q: Consider three vectors A 6) (a) Find A (B+C). Fnl A C) Find A (8C) i Find Bx(A-C)

A: Here we have  A=4i+6j-2kB=2i+7j-kC=0i+3j+5k i) find A·(B+C) ii) find A·(B×C) iii) find A×(B+C)

Q: Find the angle between the vectors a = 77 +37 +27 and 7 = 27-7+ k.

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Q: For the vectors A = ux + 3uy + 5uz, B = 2ux + 4uy + 6uz, and C = 3ux + 4uy + 5uz, show that A × ( B…

A: For the given vectors A,B,C show the given property  If A=a1ux +a2uy+a3uz and B= b1ux+b2uy+b3uz then…

Q: Consider the vectors: u=(-2,6), v=(-3, –4), w =i+9j, and x=8i-6j.

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Q: (a) 3u7 u3 (b) (c) u2 (-2u5) (d) 2u2 : (-u5)

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Q: Find the unit vector Â, B, the dot product À. B, and state whether these 2 vectors are orthogonal,…

A: Given vectors are- A→=3,-2 and B→=2,4 To find the unit vector A^, B^ and dot product A.B Unit vector…

Q: The projection of the vector 11i + Aj in the direction of the vector i+3j is the vector 2i+6j. What…

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Q: A= 2i+3j+4k, B=i-2j+3k

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Q: If a, b and c are three non-coplanar vectors, then find the value of a.(bxc) b.(cxa) c.(bxa) +…

A: Use the properties of vector box product as follows: a→.(b→×c→)=[a→ b→ c→]=[b→ c→ a→]=[c→ a→…

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A: Given a = i + j b = i - k c = i - 7k

Q: 44. (a) Find all vectors v such that (1.2.1) X = (3.L-5) (b) Explain why there is no yector v such…

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Q: (a) If a = 6i- 8j and b = i + 3j, find â and b. (b) OA = (3) and OB = (_). Find the unit vectors…

A: Some vectors are given. Based on this we need to answer some questions.