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

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Q: - - 1. If à = 2ảx + 6ảy – 3ả₂ and ☎ = −3ảx – 4ảy – 5ả₂, find a. a unit vector in the direction of A…

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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: 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: 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: The vector F = -ar + 2a expressed in RCS and in terms of is O None of the choices O - = (−cos0sind…

A: We can solve this using spherical co-ordinate matrix

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: Q.5) Determine and what is the differences between the two results. Also prove that is orthogonal to…

A: We have to find the difference between the vectors A→=-i^+8j^+4k^ and B→=i^+18j^-6k^. Also, prove…

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

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Q: 1. Consider A = 8i-12j, B = 2i + 14j and C= 18i-10j. (a) In R² space, draw the vectors A, B, and C…

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Q: Use the given vectors to find the specified scalar. u = 9i - 6j, v = -8i - 9j, w = -10i + 5j; Find u…

A: Given that     u = 9i - 6j , v = -8i - 9j , w = -10i + 5j Here we have to find u.(v+w)