Given ū = 21 -j and ỹ = 27 +3j find 3ū– 2ī.

Q: If d = i+j- 2k, b= 3i – 2j + k, č = i+j- 2k. Calculate: 1. ах (bxc) 2. || a x c ||

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Q: Given r"(t) = , r'(0) = and r(0) = . Find the j-component of r(7). Answer:

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Q: Use the equations to find dz/ðx and əz/ðy. x2 + 8y? + 9z2 = 1 Əz ax az ду II II

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Q: If v=−5i+j and w =4i+j, find |v + w|.

A: Given,           v=−5i+j and w =4i+jTo find: v+w

Q: Solve for the given DE and indicate the type of DE y" +y = csc x ) ==- 2, y" (G) y' = 3

A: Given the DE is y''+y = csc x ;   y'π2=π2-2,   y''π2=3

Q: Find the general solution. y + secx y = cos x. a. b. y' +y = (e* - e). c. y' +=y-34. с. d. y = x+y

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Q: Let a = 1-j+ k, b = 4i + 5)-k, and c - -I+j+ 4k. Find the Indicated quantity. a (b x c)

A: Given: a=i-j+k, b=4i+5j-k, c=-i+j+4k To evaluate: a·b×c Cross product of two vectors r→=ai^ +…

Q: 0(x. y) y= Vuv , then find 2. If x=, at (1,1) O(u.v)

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Q: Given = = 2y, y and x = -금Find %3D = x+1 47 O A 2r –1 -8r C DI

A: We can solve this problem by substituting or by chain rule.

Q: From v = [ 2/1 ] and w = [ 1/2 ], find the components of 3v +w and cv + dw.

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Q: r'(t) = 12e6ti + 7ej, r(0) = 2i %3D %3D r(t) =

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Q: of R using cylin S√1-², 05 of the solid B t 22 neir

A: 6. (a) The required solid is R=x,y,z: 0≤x≤1, 0≤y≤1-x2, 0≤z≤4-x2+y2. In cylindrical coordinate…

Q: Find the indicated quantity, assuming u = 7i + j, v = i - 3j, and w = 3i + 5j. (u + v) · (u – v)

A: Givenu=7i+jv=i-3ju+v=7i+j+i-3j=8i-2ju-v=7i+j-(i-3j)=7i+j-i+3j=6i+4j

Q: Simplify (ex)3. e(9x + 2) to the form e Ax + B) – eº .ex where %3D 21 B= 2 C = 2 D= 21/2 Xくくく

A: To simplify the following expression

Q: for z=1+5i and w=3+i, find z/w Write the result a+bi

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Q: iS (2) = (x + ay² – 2xy) + i(bx² – y + 2xy) is anal ytic, then the values ofa and b is

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Q: Given b = – 3i + 10j and v = 10i + 4j, find b + v. 6 + =

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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: Given z = 36t +24 and y = 252t2 + 144 da (i) dt 36 |3D dy (ii)- 504(t) %3D dt dy (iii) da (write the…

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Q: Given that y = dx dy 3u?, : 5v² and v = 2x2. U = 8. Find

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Q: Given r''(t)=4e2ti-9cos(3t)j+4k, r'(0)=2i+4k, and r(0)=i+j+5k, find the formula for r(t)

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Q: dp For p(q).= q¯³, dq -3 dw For w(u) = u7, du %3D %3D

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Q: If ā = i+j- 2k, b= 3i – 2j + k, č = i+j-2k. Calculate: 1. аx (bxc) 2. || a x c ||

A: Please see the explanation below

Q: Find the indicated quantity, assuming u = 6i + j, v = i - 3j, and w = 3i + 7j. (u + v) · (u – v)

A: We know,  i·i=1 ; i·j=0 ; i·k=0j.i=0 ; j·j=1 ; j·k=0k.i=0 ; k·j=0 ; k·k=1

Q: 3x'y"+2xy' = 0 %3D

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Q: Given r"(t) = , r'(0) = and r(0) = . Find the i-component of r(3). Leave your answer correct to one…

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Q: H.W. 1 Given that z1 = 3 + 4i, z2 = 1 – 2i, calculate: %3D 1. z1 – 22; 2. ; 3. |21|;

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find the following for the given equation. r(t) = (t? + 9t)i + (t² – 9t)j (a) r'(t) = ( 2t + 9 )i+…

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Q: Given x = 14t + 5 and y = 56t +141 %3D dr (i) dt dy (ii. dt dy (iii) da (write the simplified…

A: We are asked derivative of the given functions.  Note:-Derivative of constant function is zero.

Q: Given: x(t) = 5, 1<t<4 = 3, otherwise %3D Determine the mathematical expression for the odd…

A: Given: x(t) = 5, 1≤t≤4                    = 3, otherwise

Q: If r (t) = Give exact answers in component form. %3D a) 4 b) 7 (0) = 4

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Q: AL = 7x –6 x = AB = %3D BC = 1013 2. Point S is between R and T on RT. Use the given information to…

A: Use algebra for solve

Q: d. (V1 – 2i)7

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Q: Given r'(t) = , r'(0) = and r(0) = . Find the j-component of r(3). Answer:

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Q: To evaluate y?csc2(y³) cor?(y³)dy, we let u =cse(y³)

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Q: r(t) = 4 cos(7t)i+4sin(7t)j+3tk

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Q: GIVEN; V=3i+ 7) V = L4-47 %3D AND 1. FIND

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Q: Q1) verify the following equation:- (Ā x B )x C=(Ā.Č)B-(B.C)Ā where:- (2) point A = i-J+ 2k, B = 2i…

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Q: If ā = i+j- 2k, b= 3i – 2j + k, č = i+j-2k. Calculate: 1. ах (bxc) 2. || a xc |

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Q: Use the formula «(t) ||r'(t) × r"(t)|| to find «(t). r(t) = e12i + e-j K(t) = %3D

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Q: :Q2 / Find 1) A x B. 2) Angle Between A and B. if = 3i + 2j + 4k = 2i + 1j + 6k A

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Q: In the diagram below we have that ST B = 69° and CDU = 62°. %3D %3D E A S -V U Find: 1. ВСТ 2. ABT =…

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Q: solve fos given, dy 2. -2t "ट +-

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Q: 11. yVI – r² + /1– y? = 0 %3D

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Q: Which of the following equations are true? Select three that apply. O zi - (v2) %3D (z:)'= V

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Q: Find r(t) if r'(t) = ti+ efj + 2to2t k and r(0) = i+j+ k. r(t) Need Help? Read It

A: Given data is: r't=t2 i+et j+2te2t k r(0)=i+j+k To find the value of rt

Q: Given r(t)=t2i+5tj, find and completely simplify T(t) and N (t)

A: I am attaching image so that you understand each and every step.

Q: Given b→ =3i→-j→ and →qq→ = 6→i−3→j, find b→ + q→. b→ + q→ =  i→ +  →j

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