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Problem 2. (1 point) Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (1, 2, 4), Q = (2,3,5), and R = (2,3,6). Note: You can earn partial credit on this problem.
Consider the following. u = 7i + 9j, v = 4i + 2j (a) Find the projection of u onto v. (b) Find the vector component of u orthogonal to v.
point p lies in a rigid body that rotates at angular velocity, ω-i 7-j 10-k 5 and angular acceleration, α itj 12-k 9. The body rotates about fixed point 0, and the radius vector op is given by R-i 3-j 8-k 2. Find e acceleration of P using cross product, Unit vector i,j, and k lie in a fized coordinate system. (11 points) (a) If
(1 point) Find the points on the surface 3x2 + 4y2 3z2 -1 at which the tangent plane is parallel to the plane ) and We were unable to transcribe this imageWe were unable to transcribe this image(1 point) Consider the surface xuz48 A. Find the unit normal vector to the surface at the point (3, 4,4) with positive first coordinate. B. Find the equation of the tangent plane to the surface at the given point. Express your answer in...
9. Find the component form of the vector that starts at (3,-2) and ends at (-1,9). 10. If the terminal point of vis (4.7) and v = Ti - 13), find the initial point of v. 11. Find a imit vector in the same direction as 211 - 7. 12. Determine whether V and w are parallel. orthogonal, or neither. B. v= -2i+3j, w = -6i+9j A. V = 3i-57. w = 6i - 103 18 C. v = 3i...
Use the given vectors to find u. (v + w). u = -21 - 9j, v= - 21 + 8j, w = -5i + 5j A. - 35 B. - 103 C. -68 OD. 37 Find the unit vector that has the same direction as the vector v. v = 24i + 10j The unit vector that has the same direction as the vector v is . (Simplify your answer, including any radicals. Use integers or fractions for any nume
2. Find the closest point to y = in the subspace H = Span [ o། [ 17 [10] 3. Let B = {| 2 |,|-2, 1}. Find the coordinate vector of x = [1] relative to the [=1] [4] [2] orthogonal basis B for R3. ངོ- v1cs None of the above 5. Which of the following is true about the sets of vectors S and T? 3 1 [3 ] , 2 ), T={l U L-13] The set S...
1. A point charge +Q is located at the origin, and a point charge -Q is located at (x,y) = (0,L). (a) Find the electric field at point P, which is a distance L away from both +Q and -Q, as shown in the diagram. Express your answer in unit vector notation using the coordinate system given. (b) A point charge -2Q is placed at point P. Find the Coulomb force on the charge -2Q due to the other two...
1 Cylindrical coordinate system Given the relation of the cylindrical coordinate system r=r cos pi+r sin øj + zk (1) Lets define vectors er, eg, and ez, that indicate the direction of the vectors in the cylindrical coordinate system. Using the definition ar e = pt=r, p2 = 0, p3 (2) (a) Find a matrix for calculating er, er and e, in terms of i, j, and k. Invert the relation for expressing i, j, and k in terms of...
Find the stream function for the vector field F=36y^5/36i+9x^2/9j If C is a curve connecting the point P =(2,2) the point Q =(2,4), then the flux across C is given by: