Find the directional derivative of the function f(x,v) at point p in the direction of vector a. 1) fix, y) %3D 4x2 - хv + 5y2, р %3D (-3, -5), а %3Dі - 2; = XV A) 15/5 B) 3 515 C) 253 D) 13

Q: When the vector b = -2 is projected onto the line spanned by the vector a = 1 what is the error 2…

A: The projection of b onto a line spanned by a vector a is  b.a^=b.a|a| Given:  b=[-2-2-1]…

Q: Exercise 9: Line 1 has equations x =-1+2s , y= 1-2s and z = 1+4s. Line 2 has equations x = 1-t, y =t…

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Q: Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 1, 1) in the direction…

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Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

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: Calculate the gradient vector Vf of the function f(x, y) = x² – x + y- x²y – 2y2 at the point (2,1)…

A: According to the given information, it is required to determine the gradient vector of the given…

Q: (1) Let 0 be the angle between vectors A and B, find the value of the angle 0 when

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Q: Q/Find the real values of a , b, c that make the convolution equal to zero for the vector function…

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Q: For each problem, calculate the directional derivative in the given direction and the gradient…

A: z=x2-6y2  To Find: Directional derivative and gradient vector at P(7,2) in the direction of  a)…

Q: The unit vector in the direction of u = (2, 3) is A. (-,1) В. (3, —2) 2 3 V5' V5 3 D. (- V13 2 V13 O…

A: We a given a vector u=(2,3) We are asked to find out unit vector in direction of  vector u=(2,3)

Q: Find Vƒ(P) and D7f(P). (a) f(r, y, 2) = yf + z² – 4xz; Ū = } i – $ j+ k; P(-2,1,3)

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Q: 22. Given the symmetric equations t = - and t = +', find the vector equation of the line.

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Q: Suppose that over a certain region of space the electrical potential V is given by the following…

A: Given that, Vx,y,z=4x2-3xy+xyz Find Vx,Vy,Vz:  Vx=8x-3y+yzVy=-3x+xzVz=xy Gradient of V at P(6,6,5)…

Q: -> If the projection of a = i-2 +3k on b = 2î+ ak is zero, then the value of 2 is (A) (B) 1 - 2 (C)…

A: Use the dot product to find the projection.

Q: Given the vector function: r(t)=(√2t,e¹,e¹) find T(t), N(t), and B(t) and simplify your final…

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

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Q: Let I be the line passing through the point P=(3, -2, 1) with direction vector -[3, 2, -3]T. Find…

A: If we drop a perpendicular from a point P on a line  l then foot of perpendicular will be closest…

Q: Consider the R³ vectors v₁ = B. 3 23 V2 = 2 H -1 and v3 = D 3 (a) Find a linear dependence…

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Q: If you have vectors x-[1 5 9 5] and y-[4 8 3 6] find 1- Wex'+y 2- R-(y')* 3- X+y 4- X.*y

A: Given that we have two vectors with four components X= [ 1 5 9 5] Y= [ 4 8 3 6]

Q: Q5/A// Find the distance between the point P =(2, 1, 1) and line L:x = -2+ 5t, y= 2 +4t, z = -3-6t.…

A: Use distance formula