Suppose f(x,y) = = tan(x) + y and u is the unit vector in the direction of (-3,-1). Then, a) ▼ f(x, y) = ) Vf(-0.9, 8) = c) fu (-0.9,8) Du f(-0.9, 8) =

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Q: Let L₁ be the line passing through the points Q₁-(-1.-3, 1) and Q₂-(-4,-6, 2). Find a value of k so…

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Q: 2. Find the angle between vector [2, -5,7] and vector [6,4,1]

A: Vector [2,-5,7] and vector [6,4,1]  We have to find angle between these two vectors

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Q: Find a vector of unit length tangent to (1 + e,r tan(t)) at I 0. (금이) (1,0) (0, 1) None of the…

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Q: Find F‘(0)  for the function f(x)=3xe5x b) Given vectors a=(1,3,-2) and b=(1,1,2) , find  3a +2b…

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Q: Find the angle between the planes whose vector equations are 7-(2i + 2)- 36) =57-(3i -3) + Sk) = 3…

A: The solution to the the given question is explained below.

Q: 8. If it [13,7.-2] is orthogonal to v v=[-5, k.7], determine the value(s) of k.

A: Given query is to find the value of k.n

Q: 39. For each condition, find unit vectors å and b or explain why no such vectors exist. (a) |a+헤-0…

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Q: Let L be the line with parametric equations x-2-2t y-10-2t 2-8-21 Find the vector equation for a…

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Q: A particle moves in two dimensional space where i and į are unit vectors in the x and y directions…

A: given  r→=6t-4t2i^+2t j^ a) write down the particle's velocity vector in component form. ii) find…

Q: Use the definition to determine whether or not =(3,5,-2)'. =(-2,1,4)', and =(1,3,7) are linearly…

A: We have to check whether given set of vector is linearly independent or dependent.

Q: 2) (i) Find the direction cosines for v= he sum of their squares equals 1. (2,3,4). (ii) Verify that

A: Direction cosine and ratios

Q: Find the velocity vector v(t), given the acceleration vector a(t) = (3e¹, (Use symbolic notation and…

A: Formula for the acceleration is We have and the initial velocity

Q: Find  vector z + vector y if vector z= and vector y= . graph

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Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

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Q: 7. Consider the following two vectors: u = (5, –3) and v = (2,3) (a) Evaluate |u| and |v|. (b) Find…

A: As per guidelines, we are supposed to do only the first three parts of multipart question. If you…

Q: (14) The straight line L passes through the origin O and is in the direction i+mj. The straight line…

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Q: What three points are on the line L: vector r= (2,-5) + s(2,1), sER

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Q: Line E goes through the points (1, 5, 2) and has the direction vector ⟨2, 2, 3⟩. Line F goes through…

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Q: Determine Duf(-1,3, 2) for f (x, y, z) = e2ay° + 4x²yz in the direction (3, -2, 5). V =

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Q: Let Lz be the line passing through the points Q1=(1, 3, 1) and Q2=(7, 12, 4). Find a value of k so…

A: We will solve the problem

Q: Vectors a' and b are perpendicular to one another. Find k : a'(k², –k, 1), b´ (k, 3, – 2)

A: Scalar product of two vectors

Q: Draw the vectors in standard position in R2 with their tails at the point (2, -3).

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Q: a. A nonzero vector perpendicular to both [-1. 3, 4] and [-2. -1, 3].  b. The distance from (2, -1,…

A: Let's go through each of the questions:a. To find a nonzero vector perpendicular to both [−1,3,4]…

Q: In R, evaluate the alternating 2-form 5 = -3· dx A dy on the pair of vectors (a, b) if a = (4, 2,…

A: Given that, ξ=-3.dx∧dy on (a,b) Where a=(4,2,12),b=(-7,-4,8) The objective is to show that ξ(a,b).

Q: Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and…

A: The given problem is to find the vector equation of line that passes through the given two points.