- Format: Find the directional derivative of f(x, y, z) = -4x²z - 11 xy + 2z² at P = (-3, -3, -2) in the direction of (6, -2,0). D(6,-2,0) (-3 ab sin (a) O Search • If your answer below is a vector, input it as a column vector using the vector/matrix palette tool. • Use to explicitly indicate multiplication between variables and other variables, between variables and brackets, or between sets of brackets (e.g. x*y rather than xy; 2*(x+y) rather than 2(x+y)). . Put arguments of functions in brackets (e.g. sin(x) rather than sin x). • Give your answers in exact form. ab -3,-3,-2) What is the maximum rate of increase of f at P? |vf|(-3,-3,-2) sin (a) Ə dx = ə f W ∞ f 8 a Ω a Ω Submit Assignment N Quit & Save LxXJ Back > 0 Question M 22 D

Q: find the domain of the vector-valued function.

A: Given: rt=1t+1i+t2j-3tk

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A: Let the given vector is: v=13i+13j+13k

Q: a line is parallel to the vector i+ 5j+3k and passes through the point P = (6, 2, 4), then the…

A:

Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3,2,1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…

Q: what are the examples of contravarient and covariant tensors?

A: Example of Covariant tensor: A'i=aijAj

Q: Hiwil show that_Viz 3i+6j_and_V=-i-zj have offosite direction.

A: We have to prove that vectors have opposite direction.

Q: Let v1, v2, v3 be the vectors in R^3 defined by: v1=[0 5 8], v2=[12,-20,5], v3=[-12,15,-13] a). Is…

A: Solution: (a) We see,            v1 + v2 = [0 5 8] + [12 -20 5]                          = [0+12…

Q: Let a = (-4, 3, 4) and b = (-5, 2, 3), then find the decomposition a = a +a of a with respect to b a…

A: Ggg

Q: Determine whether the following statements are true or false. Justify your answers. (a) When u and…

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Q: How do you know if 3 vectors span R^3? Is there any example?

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Q: Find a vector orthogonal to both and . Include a step by step solution please

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Q: (b) Find the points in which the required line in part (a) intersects the coordinate planes.

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Q: What kind of transformation results in applying the rule (x, y) → (x – 5, y) in the coordinate…

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Q: A line L, passes through the points A(0, -3, 1) and B(-2,5, 3). (a) (i) Show that AB= 8 6 2 (ii)…

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

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Q: Which vector equation below represents the line in R³ that passes through the point (-4, 5, 7) and…

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Q: Which of the following sets of vectors are linearly dependent? (i) {(2,3), (-4,-6)}; (ii) ((0, 4,0,…

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Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3, 2, 1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…

Q: Let U=(-4, 3, 3) and V=(2, 1, 1). Find (2U+V), *. | (then find | (2U+V

A: Find 2U+V and it's magnitude.

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A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

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A: Given

Q: what if it was the same vector, but 5y^2j?

A:

Q: Find the scalar equation for each line: (a) a line through the point (-6, 7) with direction vector…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Consider an inner product on two P₂ vectors as (f, g) = f(-1)g(-1) + f(0)g(0) + f(2)g(2): 1) (−4 +…

A: The inner product on two P2 vectors as f,g=f-1g-1+f0g0+f2g2

Q: Write out the expressions a- Va in index notation for vector a

A: Let us consider a vectora→ = a1i^ +a2j^ +a3k^where a1 , a2, a3 are functions of (x1, x2 & x3)and…