If S is a function of (x, y, z) coordinates, and P = Ai - Bj - Ck where i, j, and k are the unit vectors, drive the following: 1. V x V. VS 2. V-VX VS 3. Vx V. P 4. V-V x P

Q: Consider the following vectors. u (6, –5) and v = (9, 1) u + v = (12, – 3) | (c) Find 7v – u. 7v – u…

A: By algebra of vectors we solve the this question.

Q: Which of the following pairs of vectors are linearly independent? Ou = (1,0) and w = (0,2). Ou =…

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Q: Determine whether the vectors u = and v = are perpendicular.

A: As we know that if the dot product of two vctors is zero then we can say that the vectors are…

Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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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: b Find all vectors W (W₁, W2, W3) that satisfy the equation: (3,1,4) x W = (-3,1,2).

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Q: Find the angle between the two vectors A = i +j+k and B = 2i+j-k

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Q: Find a real general solution x2y"+0.7xy′−0.1y=0

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Q: Find the value of a such that the vectors a and b are perpendicular where a = a î - 16 ĵ - 19 k and…

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Q: For the three given vectors, either show that they are linearly independent or find a nontrivial…

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Q: For the vectors u= ,0,2) and v= ,- 3), calculate projyu and scal, u. projy u = O DD

A: Given ,the vectors u=-4,0,2  and   v=1,3,-3

Q: A. Give the Cross products of the unit vectors (i, j, k).

A: Understanding of cross product of three vectors are required to under this.

Q: Find a unit vector v = (v1, v2, Vz3) that is orthogonal to both vectors ā = (1, 2, 0) and b = (2, 1,…

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Q: Find two different combinations of the three vectors u = (1,3) and v = (2,7) and w = (1,5) that…

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Q: Find the angle 0 between the two vectors u = and v = .

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Q: Let ū = (3,2), v = (-2, –2), and w = (-4,3). Find the vector x that satisfies 5u – v +x = 7x + w. |…

A: Given that u→=3,2v→=-2,-2w⇀=-4,3

Q: Find a vector, w, which is perpendicular to the vectors where u=61-15 Ĵ + 7k and v= -19 1+53 - 5 k.…

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Q: For the vector v = , find a unit vector in the same direction as the vector v

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Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v + w.

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Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

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