Given a point P = (2, 1, 2) and using the homogenous representation: Calculate the coordinates...

Given a point P = (2, 1, 2) and using the homogenous representation:

Calculate the coordinates of the transformed point P* if P is rotated about the X, Y, and Z axes by angles 60°, 30°, and 60° respectively.

If the point P* obtained in part (a) is to be rotated back to its original position, find the corresponding rotation matrix. Verify your answer.

Calculate P* if P is translated by d = 2i – 3j + k and then scaled uniformly by s=3.0.

Expert Solution

samet mamat answered 2 years ago

Calculate D in rectangular coordinates at point P(2, -3, 6) produced by

D3.2. Calculate D in rectangular coordinates at point P(2, -3, 6) produced by: (a) a point charge QA-55 mC at Q(-2, 3, -6); (b a uniform line charge ?ρLB 20 mC/m on the x axis; (c) a uniform surface charge density ρsc 120 μC/ m" on the plane z =-5 m.

The Cartesian coordinates of a point are given. (a) (2, −5) (i) Find polar coordinates (r,...

The Cartesian coordinates of a point are given. (a) (2, −5) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) = (b) (-2, −2) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) =...

Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point...

Plot the point whose polar coordinates are given. Then find the Cartesian coordinates of the point b. (2, π/4) c.(−3, −π/6)

Given the definition for a Point class that holds the coordinates of the point as double...

Given the definition for a Point class that holds the coordinates of the point as double values x and y, write a function called pt_dist that takes two points and returns the straight-line distance between them (as a double). Use two ways, pt_dist function version and the pt_dist method version. In main, include two if else tests for each, If passed "TEST PASSED, DIST IS " else "Test Failed, dist is ". Hint: Rhymes with Bythagorean Beorem. #include <iostream> #include...

(a) The Cartesian coordinates of a point are (1, 1).

(a) The Cartesian coordinates of a point are (1, 1). (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0≤θ< 2π. (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (b) The Cartesian coordinates of a point are \((2 \sqrt{3},-2)\).(i) Find polar coordinates (r, θ) of the point, where r >0 and 0≤θ<2π. (ii) Find polar coordinates (r, θ) of the point, where r<0 and 0 ≤θ< 2π.

The Cartesian coordinates of a point are given. (a) (−3, 3) (i) Find polar coordinates (r, θ)...

The Cartesian coordinates of a point are given. (a) (−3, 3) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find polar coordinates (r, θ) of the point, where r < 0 and 0 ≤ θ < 2π. (r, θ) = b. (5,5sqrt(3)) (i) Find polar coordinates (r, θ) of the point, where r > 0 and 0 ≤ θ < 2π. (r, θ) = (ii) Find...

The coordinates of a point P in the x-y plane are (2;3) meters. q1 = 10...

The coordinates of a point P in the x-y plane are (2;3) meters. q1 = 10 C load (1;0) , q2 = 20 C load (-1;0) is placed in the metre position. The electric flied formed by these charges at the P point, find your size and direction.

(a). The Cartesian coordinates (x, y) = (−4, 4) of a point are given. Find polar...

(a). The Cartesian coordinates (x, y) = (−4, 4) of a point are given. Find polar coordinates (r, θ) of the point so that r > 0 and 0 ≤ θ ≤ 2π. (b). The polar coordinates (r, θ) = (−3, 5π/6) of a point are given. Find the Cartesian coordinates (x, y) of this point.

4(a) Suppose a particle P is moving in the plane so that its coordinates are given...

4(a) Suppose a particle P is moving in the plane so that its coordinates are given by P(x,y), where x = 4cos2t, y = 7sin2t. x2 y2 (i) By finding a, b ∈ R such that a2 + b2 = 1, show that P is travelling on an elliptical path. [10 marks] (ii) Let L(t) be the distance from P to the origin. Obtain an expression for L(t).[8 marks] (iii) How fast is the distance between P and the origin...

2) Mark True or False for the following: The representation of a point is space, “r”,...

2) Mark True or False for the following: The representation of a point is space, “r”, is a scalar. True ___ False ___ Parameter “t” is a three-dimensional vector. True ___ False ___ When representing surfaces, the pair (t,s) points to a given point in space. True ___ False ___ In the following rotation matrix (about z), the rotation angle is -90°. True ___ False ___ 0 1 0 0 -1 0 0 0 0 0 1 0 0 0...

Question