10. In the diagram, M is the mid-point of CD, BP:PM = 2:1, AB AD = z. = x, and AC = y and %3D Express the following vectors in terms of x, y and z. (a) DC (d) BM (b) DM (e) BP (c) AM (f) AP E.

Q: Which of the following vectors are equal? s=(L-10), r=(a-by.1.2), u=(a-b.1.2). 1=(a-b) 1.2),…

A: the given vectors are: s=1,-1,0t=a-b2,1,2u=a2-b2,1,2v=sinπ2,cosπ,sinπw=a+ba-b,-12,2 we have to…

Q: Q1, Find Paametric equations for the line through the Point (0,1, 2) that is U =i 12}+ 3k and ū= 3i…

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Q: (B): Find the unit vector perpendicular to the vectors: 3i - 4j + 5k 4i + 5j-6k dw (C): If w = tan x…

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Q: Find the angle mesure between the two vectors u and v where : u=-2i + 2j + 4k, v=3i + 8j + 2k write…

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Q: 10) Find a unit vector in the direction that f (x, y, z)= 2x² +6xy² – xz' increases most rapidly at…

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Q: Q3): If A = 2i-j+ k, B = i + 2j - k and C = i + j - 2k, find unit vector orthogonal to A in plane of…

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Q: 1or Find. Ewo unit Vectors in X-y plane 30 deyree with the vectur that make angle cf V= 3i +4j ?

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Q: Find the angle between the vectors. (First: v = -21 exact u = i- 6j + k, approximate xx x +

A: topic:- vector algebra

Q: Usethe dire ctiolal devivative tohow Much F()= Cos TXy +xy" will Change if the Paint PIXiy) is Moved…

A: If z=f(x,y) is a multivariable function, then x ,y is called the input of the function, and z is…

Q: Let h ( x , y ) = ln ⁡ ( ( x + y ) 2 ) . If you are at the point ( e , e ) what unit vector makes D…

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Q: When analyzing the vectorĀ = 2i – j + 3k To the sum two vectors, the first is parallel to the vector…

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Q: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: 1) Find the MAGNITUDE and DIRECTION of the RESULTANT of ALL the forces at point A +Y -120lb APPLIED…

A: The resultant of vectors at a point is defined as the net effect of the forces acting at the given…

Q: 1 Find the velocity vector v Ct), given the aceleration vecror a Ct)= 5+2 K and the initial velacity…

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Q: Find cos(0) if 0 is the angle between the vectors u = 4i – 3k and v = 2i – 2j + k

A: Given,           u=4i+3k           v=2i-2j+k

Q: O Find a unit vector (a vector with length 1) that has the direction of 3 2

A: Given below the detailed solution

Q: A particle's position vector is given by: F(t) = R(1+ cos(wot + q cos wot))& + R sin(wnt + q cos…

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Q: 19. Suppose that the normal unit vector N of a surface S at z =f (x,y) is determined, how does the…

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Q: • We have 2x 2y Vf(x, y, z) = i+ +1)j+6k. x² + y²- 1 x² + y? – 1 | Thus Vf(1,1,0) = 27 + 37 + 6K.

A: We have to show the steps for the above equation.

Q: 6. For the vectors i and i given in problem 1, verify using the dot product that your answer for…

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Q: 6. For the vectors ü = (4, 3) and i= (-2, 3), caleulate the following quantities. (a) la+ 레 (b) la+…

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Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a…

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Q: 6. Find the work done by the force F = 31 – 5j in moving an object from the point (2, 2) to the…

A: Given that the force F=3i-5j moving from the point (2,2) to the point (7,-13). We need to find the…

Q: Find a vector normal to the plane with the given equation.3(x − 4) − 8(y − 1) + 11z = 0

A: Consider the equation of the plane: 3x-4-8y-1+11z=0.   If equation of the plane has the form:…

Q: B) Find a vector parallel to the plane 2x – y – z = 4 and orthogonal to i +j+ k.

A: This is a problem of vector analysis.. we will solve the problem using the concept of vector dot…

Q: 3. Find the length of the trajectory of the vector valued function f(t) = (7V2.1,7",e-7) from 0 to…

A: The detailed solution of the problem is given in the next steps.

Q: 4. A vector normal to the paraboloid z = (x² + y*)/2 is (a) (х, у.1). (b) (2x,2y,–1). (e) (-х,-у.1).

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Q: 19. Suppose that the normal unit vector N of a surface S at z = f(x, y) is determined, how does the…

A: Note: As company policy, we solve first question only. Please resubmit the rest of the questions in…

Q: 2.10 Express the following vectors in rectangular coordinates: 2z az (a) A = p sin o a, + p cos o as…

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Q: A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level…

A: Since you have posted multiple questions. I am answering the first three sub-parts. Please post the…

Q: -) THREE VECTORS A, B, AND C ARE RELATED AS FOLLOWS ! A AT 180°, A +C =-5+j15, 2 C = CONJU GATE OF…

A: Solution :-

Q: (b) Two out-of-phase alternating voltages are represented by: V = 3.4sin (wt +=) and V, 1.3cos (wt…

A: The given problem is to find the sum of given vectors in the form of A sin(wt+ ϕ),we have to general…

Q: Find the binormal vector for 7(t) = (3t, sint, cos t) А. ВО cost, sint V10 10 1 B(e) = (- 3 В. ВО)…

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Q: Q1A) The vectors A = 3i + j + 4k, B = 2i - 3j - k, find vector normal to A and In plane of A and, B.

A: Solution is given below:

Q: 4. Find the vector equation for a particle if A(t) = 6ti + 12t² j+ k, V(0) = 2i + 3j, and R(0) = 4k.

A: Given that At=6ti+12t2j+k,V0=2i+3j,r0=4k.

Q: 41. Find the value of A if the vectors i+ Aj+3k and-2i+j-4k arc parallel. uectors ii + 3k and 2i -

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Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

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Q: In R', evaluate the alternating 2-form 5 = -3 · dx ^ dy on the pair of vectors (a, b) If %3D a = (4,…

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Q: 2. Given the space curve .N(77). ² B r(t) = (2 cos 2t, 2 sin 21, 31), find the unit vectors, 4

A: Consider the space curve, r→t=2cos2t , 2sin2t, 3t  To find the unit vectors T→π4 , N→π4 , B→π4 Here…

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a - b)…

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Q: Using a convenient scale, find the resultant of the following vectors graphically: 10m at 40o with…

A: According to Polygon Law of forces, if a number of coplanar forces acing at a point is represented…

Q: 2) With respect to the origin 0, the position vectors of points A, B, Cand D are given by OA = 1 OB…

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Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

Q: Find the angle between the vectors i + j + 2k and 2i - j +k

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Q: (b) Solve the electric flux through a paraboloid z = x² + y² – 16 that lies below plane %3D z = 0.…

A: As per our guidelines, we can only solve first question and rest can be reposted. The solution for…

Q: The velocity of a particle is given in terms of the time t by v = sinti - 2cos(2t)j + t2k   where…

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Q: (b) Solve the electric flux through a paraboloid z = x² + y² – 16 that lies below plane z = 0. It is…

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r= 4 cos 2t and e = 5t

A: