[Question 1] Let A = p² cos()a, +sin(ø)a, + z'a¸ and B= xya, + y°a, + za¸ find 1. A•Bat (2,- 3 6 2. The angle between the two vectors

Q: What is the magnitude of the vector cos 0 i + sin 0j+ 1? 01 O2

A:

Q: Let C be the straight path from (0,0) to (7, 7) and let F = (y – z + 3)i + (sin(y – z) + 3)j. (a) At…

A: Given that,  C is the straight path from (0,0) to (7,7) andF→=y-x+3i→+siny-x+3j→

Q: QUESTION 2 The y-coordinate of the initial point of the vector v=-2i-9j whose terminal point is…

A: We will find the y coordinate as following.

Q: A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the…

A: Start from the origin, move p units to the right along the x axis and q units up along the y axis to…

Q: QUESTION 10 Let r(t)=(1-t2, 5t, 2t3). Find the z-component of the vector r'(4).

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Q: Using the vectors P = î cos 0 + ŷ sin0, Q = î cos 9 – ŷ sin o, R = â cos 4 + ŷ sin ø, prove the…

A: (a)

Q: Question 4 (a) An object is moving with position vector r(t) = cos(ot)i+sin(at)j + at³k. (i)…

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Q: 6. Find the following. a. Find the B-coordinate vector of s(t) = 4+5 sin?(t) given B = {1, sin(t),…

A:

Q: Question 6 A charged particle moving in a magnetic field will experience a magnetic force. Suppose…

A: A vector field is one in which for each point in subset of  a space a vector is begin assigned.…

Q: -2i -sj+si and -i+zi are orthogonal, then

A:

Q: (6) The position vector of a particle is F = 4i-3j+ k, It is acted upon by a force F= 21-4j+8k. Find…

A: By using definition of tarque, we find the cross product of F and r , as in next step.

Q: QUESTION 8 Consider the vectors u=(-1, 6, 4) and v=( -2, -4,-2). Find | -4u -6v |. (Type your answer…

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Q: QUESTION 1 Find the curvarure K of the vector position r(t) = %3D O A. B. Non of the above. O C. 1…

A: We need to find the curvature of the position vector rt→=2t , sint , cost The formula for curvature…

Q: Question 6 For the vector v whose initial point (-3, a) and terminal point(5,b). Also given b - a =…

A:

Q: Question 5 Find the unit vector u in the direction of the vector v= 1 %3D 5( 4, 0, 3 ) . OA U V 10 1…

A:

Q: Question 6 Find the unit tangent vector T (0) to the curve C: r (t) =2 cos(t)i +3 sin(t)j+ 4tk ©T…

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Q: 1. Consider the lines x = -1+ 2s by:- = and t2: y=s x – 5 l1 : 3 – z %3D 4 z = 5+ s а. Find two unit…

A:

Q: Question 2 For what value of t, if any, is the vector (4t, 1) parallel to the vector (4, -1) ? %3D…

A: We have to find the value of t.

Q: For a vector of my oriented at 245 degrees on the hexagonal system, find the projections of this…

A: We have to find the projection of the hexagonal system on the six leads.

Q: Eliminate the parameter from the parametric equations: x = 3 sin t y = 2+ cos t The resulting…

A: Given :                Consider the parametric equations :                       x = 3 sin t…

Q: 1/1 Determine the angles made by the vector V = 40i - 30j with the positive x- and y-axes. Write the…

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Q: 6. A particle moves so that its position vector is given by i =sin 5tî – cos 5tj , where t is the…

A: Consider the given position vector. r→=sin5ti⌢−cos5tj⌢ Now, calculate the velocity vector of the…

Q: 8. Find the position vector T(t), velocity vector v (t),acceleration a (t), and the speed for the…

A:

Q: Let θ be the angle between the vectors u = 2i + 3j−6k and v = 2i + 3j +6k. (a) Use the dot product…

A: For two vectors u→, v→ in 3-space we have that:                     u→·v→=u→ v→cos θ⇒cos θ=u→·v→u→…

Q: Problem 12. Let f be a function of r and y. Show that for any unit vector u, D-uf =-Duf.

A: Directional derivative of function f is given by

Q: QUESTION 23 Find the vector equation of the line through the point 71and perpendicular to the plane…

A: The vector equation of a plane is, a→ is the vector on the plane given and r→ is the variable vector…

Q: A particle is in motion, and its acceleration at t sec is found to be a(t) = (0)i + (2t)j + (9 +…

A: The general form of a single parameter vector-valued function in three-dimensional space is given by…

Q: Suppose 7(t) = cos(nt) i + sin(at) j+ 3tk represents the position of a particle on a helix, where z…

A:

Q: What is the magnitude of the vector cos 0 i + sin 0j +1? 00 1 O√2 02

A: We have to find magnitude of the vector cos θ i + sin θ j + 1 k  (not only 1)

Q: A person on a hang glider is spiraling upward due to rapidly rising air on a path having po- ition…

A: In this question, the velocity and acceleration vectors are determined from the position vector.

Q: 6.) r(t) = (cos t, sin t, In cos t), (1, 0, 0)

A:

Q: 2/63 A partícale which moves in two-dinensional إحراثیاته' - حركه با لبوصة motion has Coordinates…

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Q: Eliminate the parameter from the parametric equations: æ = 3 sin t y = 2+ cos t The resulting…

A: Given: x=3sint                                                                   ..1y=2+cost…

Q: 7. For vectors a and b in R? prove Lagrange's identity: ||a x b|? = ||a|| ||b||? – (a · b)?

A: for vectors a and b in ℝ2 prove -lagrange's identity a×b2=a2b2-a·b2

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: The problem below refers to a vector V with magnitude |V| that forms an angle θ with the positive…

A: Given: A vector V with magnitude │V│ and makes an angle θ with the positive x – axis. │V│= 11.6 and…

Q: 3. What is the angle between A and B if A.B=0 4. Find (u+v) (2u-v) given that uu=4 u v=-5 and v.v=10…

A:

Q: Q6) Quick answer questions: i) If y dr + dy 0 then y = i) If 1 = S, 2x e dx dy = then l= ii) Convert…

A:

Q: Question 1 Let r (t) = (sint – cos t, 3t, sin t + cos t) , t >0 denote the path of a particle in…

A: Unit tangent vector , T(t) = r'(t)r'(t)

Q: QUESTION 5 Find the unit vectoru in the direction of the vector v= 5( 4, 0, 3). O A. U V 15 1 O B. U…

A: In this problem, the first of all magnitude of the v vector is to be determine and then unit vector…

Q: Let A = -4i – 2j + 4k and B=6i – 3j. (a) Compute cos 0, where is the angle between A and B. (b) Find…

A: We have to find

Q: A positron undergoes a displacement Ai = 2.02 – 3.03 + 6.Ok, ending with the position vector f3.0j -…

A: Any position vector, r→ is represented as r→=xi^+yj^+zk^ . Let two vectors be r1→=x1i^+y1j^+z1k^ and…

Q: A particle moves so that its position vector at time t is given by r= et cos ti + e sin tj. Show…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Vector A = 4 i +4 j + 6 k  have angles α, β, θ with axis x, y, z respectively.   Write magnitude A…

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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. cos…

A: According to bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: A particle moves so that its position vector at time t is given by r = e cos ti + e sin tj. Show…

A:

Q: 7. For vectors a and b in R² prove Lagrange's identity: ||a x b||? = ||a||*||b|² – (a - b)²

A: Let's find.

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.