2.24 Given vectors A = 2a, + 4a, + 10a, and B =-5a, + аф-3a, find (a) A + B at P(0, 2,-5) (b) The angle between A and B at P (c) The scalar component of A along B at P
P (0, +a) +40 +Q Calculate the magnitude of the force F acting on +Q, and on +4Q. a. b. Draw the force vector F on +Q, and on +4Q Find the electric Field vector E at (x, y)-(0, 0) and draw it. c. d. If the third charge Qo is placed at (x, y)-(0, 0), what is the force vector F acting on Qo? (Magnitude and direction) e. Find the electric Field vector E at point P (0, +a)....
Let P = 2ax - 4ay + az and Q = ax + 2ay. Find R which has magnitude 4 and is perpendicular to both P and Q.
1. Let Q = (-3.-3.-3.3), R = (-3.-3,-33) and S = (1,10,10.1). In the following, when rounding numbers, round to 4 decimal places. (i) Find QR and RS. (ii) Find the angle in degrees between QR and RS. (iii) Find ||QŘ|| and ||RŠI. (iv) Find the projection of R$ onto QR. 2. Let v = [6, 1, 2], w = [5,0,3), and P = (9,-7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be...
Part D,E,F,G 10. Let p(x) +1. Let E be the splitting field for p(x) over Q. a. Find the resolvent cubic R(z). b. Prove that R(x) is irreducible over Q. c. Prove that (E:Q) 12 or 24. d. Prove: Gal(E/Q) A4 or S4 e. If p(x) (2+ az+ b)(a2 + cr + d), verify the calculations on page 100 which show that a2 is a root of the cubic polynomial r(x)3-4. 1. f. Prove: r(x) -4z 1 is irreducible in...
1. Let Q = (-3, -3, -3.3), R = (-3, -3, -33) and S = (1, 10, 10.1). In the following, when rounding numbers, round to 4 decimal places. (i) Find QŘ and RS. (ii) Find ||QR|| and ||RŠI. (iii) Find the angle in degrees between QR and RS. (iv) Find the projection of RŠ onto QŘ. 2. Let v= [6, 1, 2], w = [5,0,3], and P = (9, -7,31). (i) Find a vector u orthogonal to both v...
Let R = A sin q, where A is a fixed constant and q is uniformly distributed on (pi/2, pi/2). Such a random variable R arises in the theory of ballistics. If a projectile is fired from the origin at an angle a from the earth with speed n, then the point R at which it returns to the earth can be expressed as R = (v^2/g) sin 2a, where g is the gravitational constant, equal to 980 centimeters per...
2) Determine the direction and magnitude of the electric field at the point P shown in the figure. The two charges are separated by a distance of 2a. Point P is on the perpendicular bisector of the line joining the charges, a distance x from the midpoint between them. Let a = 1.0 m, x-8.0 m, and Q= 5.0 uc -0
1) Find the electric field vector E at point P= (0,-a). (Calculate the magnitude and draw the vector). 2) Sketch the electric field lines. 3)Find out the location (x,y) where the electric field E becomes 0. -Q (0, a) 2Q P (0, -a)