The point P has coordinates a = 1 m and y = -1 m relative to the origin O and the vector v is as shown. P Draw the orthogonal projection of v onto the vector ê, associated with the polar coordinates for point P.

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: Find the vector parametric equations for the line. in the direction of the vector – i+ 5j-3 k and…

A: equation of line in vector parametric form

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

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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: Give a vector parametric equation for the line through the point (3, 1) that is perpendicular to the…

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Q: Let P be the point (1, 1, 4). Find the parametric equations of the line through P and parallel to…

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Q: Given the point D(-4,5,3) and A = ya, + (x + z)z dy, express the D and A in: Kindly answer in vector…

A: Given the point D=-4,5,3 and A→=yax→+x+zzay→. To express D and A→ in: 1. Cartesian Coordinate system…

Q: Find the image of the vector (1, 1, 1) for the rotation.30° about the z-axis

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Q: Find the polar coordinates, 0 ≤ θ < 2p and r ≥ 0, of thefollowing points given in Cartesian…

A: Cartesian coordinates. (-3, 4)=(x, y) Polar coordinates (r, θ) = ?        where  0 ≤ θ < 2pi and…

Q: Find parametric equations for the lines in The line through the origin parallel to the vector 2j + k

A: Given  The vector equation is  0i +2j+k  The line passing through origin , origin is  ( 0 ,0 ,0)…

Q: Find the Cartesian coordinates, (a, b), of the point given in polar coordinates by Р(2, п /3). 1.…

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Q: Find the length of the curve r = 2 sin^3 (u/3), 0 … u … 3pi , in the polar coordinate plane.

A: Given:        r=2sin3u3,  0≤u≤3π

Q: In the figure, a vector a→ with a magnitude of 24.1 m is directed at angle θ = 68o counterclockwise…

A: Given that: Magnitude of a→ =24.1mAngle of a→ w.r.t. coordinate axes: θ=68°Angle of primed…

Q: O Find the parametric equation of the line through the point (-3,1,6) parallel to the vector V 2i +…

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Q: Find the equation for the plane through the point Po = (2,3,8) and normal to the vector n= 3i + 8j +…

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Q: Find a vector v parallel to u=4i−3k and with magnitude ||v||=4

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Q: In using polar coordinates for plane curvilinear motion the time derivatives of the unit vectors e,…

A: In polar coordinates: x=rcosθy=rsinθz=z where, r=rr^θ+k^z

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 vector whose magnitude is 5 and which is in the direction of the vector 4i- 3j + k. Q.2

A: Since you have asked multiple question As per our policy, we will solve the first question for you.…

Q: Find the parametric equation of the line that passes through the point P(2,4, –2) and is parallel to…

A: Parametric equation of line that passes through the point P(x0, y0, z0)& parallel to vector a =…

Q: Find equivalent polar coordinates (r', 0') satisfying r' ≥ 0,0 ≤ 0¹ < 2π for the · (-1, (c) point…

A: Solution is given below:

Q: Express the given parametric equations of a line using bracket notation and also using i, j. k…

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Q: The side of S is given by x² + y = 16, and its height is 4. (a) Give a parametric equation, r(t) for…

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Q: Find the vector parametric equations for the line. in the direction of the vector 57-5-k and through…

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

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Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec u.

A: The relation between polar coordinates r,u and rectangular coordinates x,y is x=rcosu…

Q: The vector diagram at the below shows the displacement between the cities as AB (magnitude A - 80.0…

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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 a vector.

Q: In graphics draw the Unitary vectors that we use in curvilinear movements: a) In Polar coordinates…

A: To draw: The unitary vectors that we use in curvilinear movements in: (a.) Polar coordinates (Radial…

Q: Find the equation for the plane through the point Po = (5,4,6) and normal to the vector n= 2i + 3j +…

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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: Find the polar coordinates, 0 ≤ θ &lt; 2π and r≤ 0, of thefollowing points given in Cartesian…

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Q: Find the polar coordinates, 0 ≤ θ &lt; 2p and r ≥ 0, of thefollowing points given in Cartesian…

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Q: Find the image of the vector (1, 1, 1) for the rotation.60° about the y-axis

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Q: Find polar coordinates with positive r and 0s 0 < 2n for each of the four points. (x, V) = (,8 (a)…

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Q: If a line is parallel to the vector 8i + 5j+3k and passes through the point P = (6,2, 4), then the…

A: The line which is parallel to the vector  ai + bj + ck and passes through (x1 , y1 , z1) has the…

Q: Consider the following graph. (4,5) 2 (1, 2) 3 (a) Find the component form of the vector v. (b)…

A: Given vector is as shown below :

Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, −1,…

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Q: Given the vector function: 7(t) = (e', e' sin(t), e cos (t)) Determine the equations of the normal…

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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…

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Q: The figure below open cylindrical can, S, standing on the ry-plane. (S has a bottom and sides, but…

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Q: 4-1. Locate the tip of a one-link robot of 10 in. length as a 2-D position vector with a direction…

A: We have to find x and y components and write its polar and rectangular forms

Q: Question 3 Determine which vector from the options below is in the plane: 1 I = S + tl 2 - TO Omo

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Q: 2. Find an unit vector perpendicular on both a =i +2]- and 6 2i -k.

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

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

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Q: Drag the blue point to a location on the coordinate plane so that the vector v (shown below in blue…

A: Given: Magnitude is 17 and the direction is 28.07° The main objective is to find the vector r→…

Q: Find a vector equation and parametric equations for the line segment that joins P to Q, given P(0,…

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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