Let f(x, y) = x6y4. Round the components of your answers to three decimal places. (a) At the point (- 2, 1), find a unit vector in the direction of maximum rate of change. i i + i (b) At the point ( – 2, 1), find a unit vector in the direction of minimum rate of change. 7 + i i 7

Q: [P] 3 as a sum of one vector from x-axis and one from the y-axis. 8. 3. Write the vector u =

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Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: Definition used -                       If we have to write a vector as a linear combination of…

Q: Find u · v. u - (7, 2) - (-6, 3) V u.v -

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Find the vectors direction of F= -2yi-xJ of the points below :- (-12-1), (-21-1),(3,0). (-1₁-2),…

A: Vector, F→=-2y i^-x j^Points: -1, -1, -2, -1, 3, 0, -1, -2, -3, -2, -1, 0

Q: X = Find the vector equation for the line of intersection of the planes x − 5y + 5z = −5 and x + 5z…

A: Given the equation of planes x-5y+5z=-5 and x+5z=1. To find the vector equation for the line of…

Q: has an initial point (-3, -6) and terminal point (4, 5). Write as a linear combination of the…

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Q: Write the vector-valued function for the line containing (2.6,7) and (-4,-1.2). Use the equation…

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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: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: The concentration of salt in a fluid at is given by mg/cm . You are at the point . (a) In which…

A: In this question data is missing here so I am taking data as pr my concern, you can put your data in…

Q: M] - [8] x+y -3x+y.

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Q: Determine the graph corresponding to the given vector equation. r(t) = (²-1)j +2tk, -1sts1 Choose…

A: Given that r(t)=(t2-1)j^+2tk^ , -1≤t≤1. Put t=-1, we have that r(-1)=((-1)2-1)j^+2(-1)k^ =-2k^ Put…

Q: Determine the direction in which f = x²y√z has maximum rate of increase from P = (8,3,8). Express…

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Q: et L₁ be the line passing through the points Q₁(-5, 2,-5) and Q₂(-14, -7, 1) and let L₂ be the line…

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Q: X = Find the vector equation for the line of intersection of the planes x - 5y + 5z = −5 and x + 5z…

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Q: perpendicular to (x, y, z) = (1, -2,0) + r(1, -1, 1) through P(1, 3,5) [parametric equations]

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Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

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Q: 5. In each case, find the x- and y-components of vector : (a) ā = 3.20 + 6.50j; = (b) Â =18.2j…

A: Given that the vectors a  A→=3.20i^+6.50j^b  A→=18.2j^-7.91i^c  A→=-12.0i^+21.2j^d  A→=5.0B→  where…