A vector can be represented by its rectangular coordinates x and y or by its polar coordinates r and θ1 and θ2 . The relationship between them is given by the equations:  x = r * cos(θ1) y = r * sin(θ2) where -2π ≤ θ1 ≤ 2π and -π ≤ θ2 ≤ π . Assign values for the polar coordinates to variables r and theta. Then, using these values, assign the corresponding rectangular coordinates to variables x and y.

Q: Find the angle between the vector through the origin & the point (1,1,1) and the component of Ā = 2i…

A: Given:-A vector passes through the origin & the point (1,1,1) A→=2i+2j-k and B→=i+j To Find:-The…

Q: For The sperical polar coordinates prove that their unit vectors are mutually orthogonal?

A: There are three kinds of coordinate systems to plot a point or a curve namely the cartesian…

Q: The horizontal component of vector a is equal to the vertical component of vector 6. If 30° is the…

A: Components of a vector v→ :  Horizontal component is v→ cos θ Vertical component is v→ sin θ where θ…

Q: A passive rotation by an angle of a vector v in the xy-plane, measured counterclockwise in the…

A:

Q: Convert the vector Ả = = pzsino a,+ 3pcos¢ a p + pcosø sinø az to RCS. Simplify your answer and show…

A: A vector in cylindrical coordinates can be written as A→=Aρaρ⏞+Aφaϕ⏞+Azaz⏞ A vector in cartesian…

Q: Let 0 be the angle between the vectors u = 2i + 3j - 6k and v = 2i + 3j + 6k a. Use the dot product…

A:

Q: Find the angle θ between the vectors a=5i−j−4k and b=2i+j−4k. Answer (in radians)

A:

Q: Find the angles between the vectors to the nearesthundredth of a radian. u = 2i - 2j + k, v = 3i +…

A:

Q: Find the angle between the vectors u = ⟨3, 1⟩, v = ⟨2, −1⟩     (a) in radians and (b) in degrees.

A:

Q: If a = 3i +j - 2k and b = 5i –j- 2k, then find %3D а. а xb b. vector resolute of vector a in…

A: We will find out the required values.

Q: The point P has coordinates a = 1 m and y = -1 m relative to the origin O and the vector v is as…

A: Orthogonal projection of a vector is component of a vector along a direction perpendicular to the…

Q: 3) Find the components of the vector i that has a magnitude of |0| = 9750N and direction 0 = 243.0°-…

A: Find the components of vector v. |V| = 9750 θ= 243.0o

Q: Find the cosine of the angle between the vectors P1 (x) = 1 + 2x – x² and p2 (x) = 2 – 3x – 2x² with…

A: We have to solve given problem:

Q: Find the unit vector in the same direction as v = 4i - 3j. Then verify that the vector has magnitude…

A: Consider the following vector: v→=4i^-3j^ Consider the following formula: unit…

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: Find the angle 0 between the vectors in radians and in degrees. - co) + sin() = cos 4 u = cos i +…

A:

Q: 2. Start with the vector =(2, 1) a) Rotate the vector 55° counterclockwise and sketch the resulting…

A: Given: The vector x→=2,1. To find: a) the resulting vector after rotating the vector x→ by 55o. b)…

Q: 4 3 Let U 4 and V = - 5 - 3 -2. Find the angle between the vectors (in radians).

A:

Q: 1. Find a unit vector pointing in the same direction as v = 2i – k.

A:

Q: Find the angle between two vectors a = (3,4,0) and b = (4,4, 2). O a. cos Cos cos-() O d. cos-() Ос.

A:

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

A:

Q: Find the angle between the vectors u = cos( /6)i + sin( /6)j, v = cos( 3/4 )i + sin(3/4 )j     (a)…

A: u=cosπ6i+sinπ6j,  v=cos3π4i+sin3π4j Now,…

Q: Calculate the cosine of the angle which the vector 2i+2j-k makes with the positive x-axis

A: Given: find the cosine of the angle which the vector 2i+2j-k makes with positive x axis

Q: A plane with an airspeed of 450 miles per hour is flying in the direction N35°W.A vector is…

A: Concept:   The calculus helps in understanding the changes between values that are related by 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: The vector diagram at the below shows the displacement between the cities as AB (magnitude A - 80.0…

A:

Q: Find the angles between the vectors to the nearesthundredth of a radian. u = √3i - 7j, v = √3i + j -…

A: Given:u=3i-7jv=3i+j-2kAngle:cosθ=u→.v→u→.v→

Q: The angle between the vectors A = 2j -3j +1k and B = 4i -3j +1k, in term of cos@ is !!

A: We use the definition of angle between two vectors to find the angle between the vectors A and B.

Q: nd the an

A: Here we have, u→=cosπ3i+sinπ3j ........................................ (1)  v→=cos3π4i+sin3π4j…

Q: If is a covariant vector in Cartesian coordinates x',x. Find its components in polar coordinates , x…

A:

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: a. Find vectors nį and n2 that are normals to II and IL respectively and explain how you can tell…

A: The planes are given by π1: x1x2x3=0-33+λ11-12+λ2313 and π2: x1x2x3=000+μ112-1+μ2340. For π1:…

Q: 1. Find the angle that the vector V = makes with the positive x axis.

A:

Q: Mathew wants to throw a bouncy ball at the ceiling so that it bounces down and lands on Wiley's…

A:

Q: If the position vector of a particle P is r(r) (3cos t,5sin7,4 cos t) a) Show that the speed of the…

A:

Q: What is the unit-vector notation for each of the following vectors, all with magnitudes of 33.5? (a)…

A:

Q: find the component form of the vector. The vector obtained by rotating [0, 1] through an angle of…

A: We have the vector is (0, 1)   We have to find the vector obtained by rotating (0, 1) through an…

Q: Find the angle between two vectors a = (3,4,0) and b = (4,4, 2). %3D cos-(금) O b. cos-) c. cos) O d.…

A: We need to find the angle between the vectors a=(3,4,0) and b=(4,4,2) We know a·b=|a||b|cos(θ) here…

Q: In the diagram below, a and b are vectors such thay cos0 = 1/6. Given thay a= i +j+ pk and b= 2i…

A:

Q: Find the angle 6 between the vectors. u- (1, 1, 1), v- (5, -4, 3), radians

A: Angle between the two vectors can be found by applying dot product of two vectors.

Q: find the component form of the vector. The vector obtained by rotating <0, 1> through an angle…

A: Find the component form of the vector. The vector obtained by rotating <0, 1> through an angle…

Q: 3. If Å = +2.00m i - 3.00m k and = -4.00 mi - 3.00m k , find the resultant R = A-C using component…

A: Use the component method to find the difference of the vectors.…

Q: Find the unit vector in the same direction as v = 5i - 12j. Then verify that thevector has magnitude…

A: Unit vector in same direction vectorvector's magnitude

Q: 1. Find the angle between two vectors ā and 5 with magnitudes 3 and 2, respectively having ā-5 = J6…

A: Given,            Magnitude of a→ and b→ are 3 and 2 and their dot product is a→·b→=6.To find : The…