With v = (1, 1) and w = (1, 5) choose a number c so that w - cv is perpendicular  to v. Then find the formula for c starting from any nonzero v and w.

Q: Q5: a. Find * and for u - p=x+y+z ,and q = x+ y+ z, and r=x+y-z, at the point (x,y, 2) = (v3, 2,1).…

A: a)                          u=p-qq-r                             p= x+y+z;…

Q: Given o = y x² + 2y – z and ū = î – 3ĵ + 2k , i ƒ Vþ at the point (1, 1, 1) is perpendicular to ū,…

A: Given two vectors, ϕ=γx2+2y-z and u→=i -3 j +2 k. To determine ∇ϕ. ∇ϕ=2γx i+2 j-k Now at the point…

Q: Complete the proof that ZYXZ SUT. P Q R. U W Y

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Q: Given f(r, y) = yln(5z+ y), find .(e, v) - 1,(2, u) = %3D

A: We have to find derivative

Q: for for w= rs ,Y=uV S=uーv, find and Jw

A: Given w=rsr2+s2, r=uv, s=u-2v To find  ∂w∂u and ∂w∂v By chain rule,…

Q: Given w = xysin(z²), x= s-t, y = s², z= t². Find ay

A: Explanation of the answer is as follows

Q: If X and Y are independent RVs with f (x) = e U (x) and f,(y) = 3e¯" U ( y), e-3y find f.(z), if Z =…

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Q: The points J, K, L and M all lie on the same line segment, in that order, such that the ratio of JK…

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Q: Let ƒ(x, y) = x2 - xy + y2 - y. Find the directions u and thevalues of Du ƒ(1, -1) for which Duƒ(1,…

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (e) z = exs ; x = s2 + 2st, y = 2st + t2

A: Given:To Find (∂z)/(∂s) and (∂z)/(∂t)(e) z = exs  ; x = s2 + 2st, y = 2st + t2

Q: Find the values of for which (40-4.0)ndV =(a,) la.1) are linearly independent in

A: Two vectors are linearly independent iff the matrix formed by placing the coordinates of each vector…

Q: 4. Evaluate S. (z – 4) dz, where r is a contour from the two line segments, the first from z = -3 to…

A: Contour integrals or line integrals along a path C   can be written as ∫Cf(z) dz=∫abf(z(t) z'(t) dt…

Q: If a particle is moving with v(x)=1.5(x^1/2) and s(9)=33, what is the position of the particle? As a…

A: Let v(x) denote the velocity of the particle and s(x) denote the position of the particle.Obtain the…

Q: AISO is isosceles with IS = IO. 22 = 2x+24, mZ3 = 6x– 52, %3D %3D nd mZ1. 1/ 3 bX 2 bx -52-180 S x-…

A: We have to solve the problem

Q: If (x, y) = (-V3, 1) , then find r and 0.

A:

Q: 26. If RX = 6z+2, XS 18, and RS = 14z, find z. j %3D %3D

A: Recall: If XY is line given such that XZ=a ; ZY=b and XY=c then  XY=XZ+ZY   ⇒a+b=c   Note :…

Q: 1. If 4=x'zi-2y'?'j+xy'zk , find div4 at points (1, -1,1).

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Q: 6) Given that h(x,y) = e**y® _ ¥² Find hxx, hxy, hyy, hyx

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Q: find the value(s) of a making v⃗ =7ai⃗ −3j⃗ parallel to w⃗ =a2i⃗ +6j

A: We have to find the values of a

Q: if y=sin (x), z=cos (x), v=exp(x), where could you plot y, z, v as shown below!

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Q: Find the length of the spiral r = eθ/√2 from θ = 0 to θ = π.

A: Given Differentiating r with respect to thita ,we get

Q: Find ∂z / ∂v using the chain rule if z = sin(x/y), x = ln(u), and y = v. Put the answer in terms of…

A: Firstly, we find partial derivative of z with respect to x and y, partial derivative of x with…

Q: dz dz and at the point (3, 6, 1) where z is defined implicitly by the equation z4 + z?x2 - y - 4 =…

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Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (c) z = x2 + 2y2 ; x = es - et, y = es + et

A: Formula to find the partial derivatives helps to find the partial derivatives of the function with…

Q: To give the first digit x the second digit y, three points are given as follows: (0, 0), (ax, ay),…

A: The given points are 0 0 ax ay bx by

Q: a A = and if xy = 1, then det ( AAT ) is equal %3D to y a

A: Given:A=axyaif xy=1 then detAAT=?

Q: f({x, y))) for all c e R and all (x, y) E R?

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Q: If y = x2 +1 and u= Vx? + 1, then at x = V3 equal to du 1 -4 -1

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Q: If X and Y are independent RVs with f (x) = eU (x) and f,(y) = 3e U(y), -3y X find f.(z), if Z = Y

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Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: Given f(r, y, z) = – 5e 4ayz, find %3D fr(x, y, z) = f,(x, y, z) = f:(2, y, z) =

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Q: Given: z = = x* + zy°, * = ww* + w, y = u +ve" a z Find when u = - 3, v = 2, w =

A: Given: z=x4+xy3x=uv4+w4y=u+vew The objective is to find ∂z∂u, when u=-3, v=2, w=0

Q: If = 2 z-x'y and A = 2x'î-3 yzj +x z'k, find A.V and A xV4 at the point ( 1,-1,1).

A: given ϕ=2z-x3y and A=2xi^-3yzj^+z2 k^ find at the point 1,-1,1 1) A·∇ϕ 2) A×∇ϕ

Q: if z is dirctly proportional to the product of x and y and if z is 6 when x is 3 and y is 4, then…

A: Solution is given below..

Q: T (x, y) (2x,y) is an is %3D

A: T(x,y)=(2x,12y) The transformation of any figure changes the size, shape and the position to create…

Q: Write proofs in two-column form.

A:

Q: Given: y2, = uv4 + w*, y = u + ve"| z Find when u 1, v = 3, w = 0

A: We know:

Q: R and r are defined by E(r, – 5)(y – T) Sry VS., Syy SSR R2 r = SST' (1) Show R? = r².

A: If y = a+bx is the linear equation  Correlation attempts to measure the strength of the relationship…

Q: Given f(r, y, z) = x cos(y- z), find: (a) (c) (b) (d) drðydz

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Q: Given Yy - y = – ỹ Yy - y + y. - ỹ and (y — У )? [(Yj – J,) + ỹ, – ỹ )]² 2. %3D

A: Given that

Q: If E?uz = x² and h = 1, then find ux. %3D

A: The objective is to find ux. Given information is: E2ux=x2, and h=1.

Q: In general, E(XY) + E(X) × E(Y), but if X and Y are E(XY) = E(X) × E(Y). independent RVs,

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Q: Determine C, and C, so that y(x) = C, e²* + C,e* + 2sinx will satisfy the conditions y(0) = and…

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Q: Find the gereral Solution of the fille d dffferential equation. 3,n1 %3D | -

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Q: If f(x,y,z)=exp(3x)cos(-4yz), find Vf. %3D

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Q: Given f(x, y, z) = x In(yz³), find fay and fyz. %3D

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Q: If w = xy + yz + xz , x = u + v, y = u – v, and z = uv (;1). d) 글 find at the point ( u, v) = ,1).…

A: Given that w=xy+yz+xz , x=u+v , y=u-v , z=uv find ∂w∂v at the point u,v=12,1

Q: If C is the line segment from (8, 4) to, (0, 0), find the value of the line integral: (6y? i + 5x})…

A: To solve the line integral from (8,4) to (0,0)

Q: P to the line L is equal P that is orthogonal to t

A: Given as, The distance is given as, d=AP→sinθ

Q: Given: z = a? + xy*, x = uv² + w*, y = u + ve" dz Find when u = - 2, v = 1, w = 0 du

A: