Q.1 Find a.b and a x b a =i+j+k b= - 5i + 2j– 3k Q2 Find the cosine of the angle between the vectors: a = 4i + 2j-k b=2i+4j-k Q3 Find real numbers x, y and z such that (x + 4)i + (y – 5)j + (z – 1)k= 0

Q: Define vectors v = 3i - 2j and w = -2i + 4j. Blank 1: Find w - v. Blank 2: Find ||2v+w|l.

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Q: Vectors u and v are shown in the graph. -12 -11 -10 -9 -8-7-6 -5 -4-3-2 What is projvu? u 6 5 3 2 -1…

A: Graph

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 the cross product a × b. a = j + 9k,    b = 4i − j + 2k       Verify that it is orthogonal…

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Q: Find the angle between two vectors ū = (1, –1,0), and ở = (2, –1,2) %3D

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Q: Determine whether v and w are orthogonal given v=-5i+2j and w=2i-4j

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Q: Use complex numbers to transform the following vectors, rotating by the angle and scaling by the…

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Q: Find Vz. 3ce3y x + 8y NOTE: Give your answer in unit vector notation; that is, in terms of i and j.…

A: given  z=3xe3yx+8y   and we know  ∇z=∂z∂xi→+∂z∂yj→…

Q: 2. Let A (1,-1,0) and B = (2,1,-2). (a) Solve for projgA. (b) Find the angle between projgA and A.

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Q: Select the option that gives the vector product of i+k and i + j Select one: 01 Oi+j-k Oi-j-k…

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Q: Find the triple scalar product (u xv). w of the given vectors. u= -5i - 3j+ 4k v=5i - 8j + 4k…

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Q: Find the cross product a x b. a = j + 6k, b = 3i - j + 5k Verify that it is orthogonal to both a and…

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Q: 2. If a --i+3j-k and E-2itj-3K decompose vectoes E into the sum of two vectors, one is paralled and…

A: This question can be solved using the concept of condition of two vectors to be parallel and…

Q: Find the triple scalar product (u xv). w of the given vectors. u= -51-3j+4k v=8i-10j + 2k w=31-6j-7k

A: The given vectors are u=-5i-3j+4k, v=8i-10j+2k and w=3i-6j-7k. We have to find the value of the…

Q: Find the cross products u xv and vxu for the the vectors u = 2i-j-2k and v= i +3j - 3k. U XV= i+ j+k…

A: (.) Given vectors are,      (.) Corss product of two vectors  and   is given by,           &…

Q: Determine if the given vectors are orthogonal. a. v = 3i – 6j and w = 8i + 4j b. s = -2i – 5j and r…

A: Consider the pair of vectors  a)v=3i−6jw=8i+4j b)s=−2i−5jr=−4i+8j

Q: Express the vector as a product of its length and direction. 21+4j+4k O A. 6 OB. 6 18 + gi+? OC.…

A: The given vector is  2i + 4j + 4k we have to express vector as a product of its length and…

Q: Given the vectors A = (–2, 1, 3), B = (–5, 3, 0) in R³, then B x A is 9i - 15 j + k -9i - 15 j - k…

A: Vector cross product

Q: For what values of a are the vectors (4, -2, a) and (9, a², a) orthogonal? O -6 and 6 0 O -2√3 and…

A: Equate dot product of two vectors to zero

Q: are parallel, orthogonal, or Determine whether vectors V and W neither. If parallel, determine…

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Q: If c = 14, is the vector 2i + 5j in the span of ci – 12j and 7i - 6j? If c # 14, is the vector 2i +…

A: Answer