Let P = 2ax - 4ay + az and Q = ax + 2ay. Find R which has magnitude 4 and is perpendicular to both P and Q.
are Prove that Ā = 4ax – 2ay – az, B = ax + 4ay – 4az perpendicular to each other.
Q3/A Prove that Ā = 4ax – 2ay – az, B = ax + 4ay – 4az are perpendicular to each other. Q3/B Answer the questions with True on the right phrase and false on the wrong phrase with correct the wrong if you found it. Answer five only 1. – sin Ø Is the result of dot product for unit vectors ā, dotāz. 2. Vector field that each point in its region is described by a magnitude as well...
Q3/A Prove that Ā = 4ax – 2ay – az, B = ax + 4ay – 4az are perpendicular to each other. Q3/B Answer the questions with True on the right phrase and false on the wrong phrase with correct the wrong if you found it. Answer five only 1. – sin Ø Is the result of dot product for unit vectors ā, dotāz. 2. Vector field that each point in its region is described by a magnitude as well...
2. Given A -4ax 2ay 3az and B 3ax 4ay az, find a. magnitude of 5A 2B b. a unit vector in the direction of (5A - 2B)/IA c. the vector component of BA that is parallel to B, and d. the vector component of A that is perpendicular to B |(5 points) a. 31.12 (5 points) b. -0.83a,-0.064ay0.54az (5 points) c. -0.807ax 1.076ay +0.269az (5 points) d. -3.19a, 3.07ay 2.73a 2. Given A -4ax 2ay 3az and B 3ax...
1.28 Let P 2a, 4a, + a, and Q a +2a, Find R which has magnitude 4 and is perpen- dicular to both P and Q. / 1.29 Let G-xa-ya, + 2za, and H :-уга, + 3a,-xza.. At point (1,-2, 3), (a) calculate the magnitude of G and H, (b) determine G.H, (c) find the angle between G and H. 1.30 A vector field is given by H 10уга,-8xyza, + 1raz
ax az . Letſ be a differentiable function of one variable, and let w = f(p), where p = (x2 + y2 + 2)/2. Show that dw ay · Let z = f(x - y. y - x). Show that az/ax + az/ay=0. Let f be a differentiable function of three variables and sup- pose that w = Sex - y. y - 2.2 - x). Show that aw ду az Page 1 / 1 aw aw ax + +...
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...
Let P(0,1,0), Q(2,1,3), R(1,-1,2). (la) Compute PQxPR. (1b) Find the equation of the plane through P, Q and R in the form ax+by+cz=d (10) What is the angle formed by this plane and the xy-plane? Please answer ic.
(1) Equation of a Plane Let P(1,1,-1), Q(1,2,0), R(-2,2,2). (la) Compute PQxPR. (1b) Find the equation of the plane through P, Q and R in the form ax+by+cz=d. (10) What is the angle formed by this plane and the xy-plane?
:| Let T : P → R , such that T (ao +ax+a2x2 +a3r)-4 +ai +a, +a3 . a) Prove that T is a linear transformation b) Find the rank and nullity of T. c) Find a basis for the kernel of T. :| Let T : P → R , such that T (ao +ax+a2x2 +a3r)-4 +ai +a, +a3 . a) Prove that T is a linear transformation b) Find the rank and nullity of T. c) Find a...