2. Determine whether the following vectors are linearly dependent in R³: (O)--- ()--C) 1 , = , ez = 0 0 0 1 (a) e₁ = 0 2 ·()· · - () -- () --- () -- () 2 , V = W = (c) u = V= 2 1 1 1 -2 (b) u = (d) u = (-)--(-)--() 2 V= W = 0 6 -3 6

Q: 13. Find a vector equation of the line through (2, 1) parallel to (x, y) = (-2,7)+t(3,5). 14. Find a…

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Q: Let B be a subset of R4. Which of the following statements are correct? If |B| = 5, then B spans R4…

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Q: 8. A line e is parallel to the vector 2i- 2j + k and passes through the point A with position vector…

A: The plane's normal vector is 3i-4j-k  and a position vector passes through it is  -i+4k. The vector…

Q: 4. State with a brief explanation whether the following statements are true or false. (a) The…

A: a) true The vectors (1 ,0) and (0,1) is linearly independent. We know that linearly independent set…

Q: If r(t) = u(t) x v(t), where u and v are the vector functions given below, find r'(2). u(2) = (6, 3,…

A: To find r'(2).

Q: C

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Q: (c) Find the distance between the two points u = (9, -3, 4) and v = (−3, 2, 5). (d) Find the norm of…

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Q: Suppose f(x, y) = (a) ▼ f(x, y) = (b) ▼ f(-0.7, 7) = tan(x) + y and u is the unit vector in the…

A: Given that f(x,y)=tan(x)+y  and u is the unit vector in the direction of <2,3>now, ∇f(x,y)=fx,…

Q: Suppose f(x,y) = = tan(x) + y and u is the unit vector in the direction of (-3,-1). Then, a) ▼ f(x,…

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Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: (1)-(9-1²₁.sin(√²²-9)). Find the domain of the vector function, r(t):

A: To find the domain of the given vector function

Q: Suppose f(x, y) = (1, -3). Then, (a) Vf(x, y) = (b) Vƒ(1,5) = (c) fu (1,5) = Du f(1,5) = x² + y² and…

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Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

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Q: Let u = (2, 1, -2), v= (0,3,-5), and w = Compute the indicated vectors. (a) u × v = (?, ?, ?) (b) -…

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Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: 3. Find a parametrization for (a vector valued function that traces) the line which passes through P…

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Q: Where does the line with the vector equation [x,y,z] = [6, 7, -8] + t[-2, 4, 1] intersect the…

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Q: 7. On a two-dimensional plane, sketch the vector |v>= such that it emanates from the coordinate…

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Q: 3. A point P(3,0,5) lies on a plane that can be defined by the scalar equation Ax+By+Cz+ D = 0. A…

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Q: Suppose f(x, y) = √tan(x) + y and u is the unit vector in the direction of (1, 1). Then, (a) ▼ ƒ (x,…

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