9) Suppose that the plane given by 3x + 4y - 12z=2 contains the point P...
АЗ. You are given that the plane P contains both the point and the line Ls, where Q has position vec- tor q = i + 3, and L3 is given by the equation r = (0, i, 2) + λ(1, 3,-1) (where λ is a real parameter). i) Write down two vectors representing two different directions which lie in the plane P. [2 marks i) By using the cross product or otherwise, find a direction perpendicular to the plane....
please help ! Q1-Q6
1. Let F (3x - 4y +22)i+(4x +2y 3z2)j + (2xz moving once around an 4y zk be a vector field. Consider a particle ellipse C given by parametrization r= 4 cos ti +3 sin tj. Find the work done. 3 3 = 3, y=-- and 2 1 2. Let D be the region in the first quadrant bounded by the lines y=-r1, y 4 + 1. Use the transformation u 3 2y, v r +...
Question 9: Plane through point and line A plane contains the point P(-1,2,3) and the line L(t), where L(t) is given by equation (2, 4t - 3,1 – 4t). Find the equation of this plane. Type in the equation of the plane with the accuracy of at least 3 significant figures for each coefficient 1 ) x + ( Dy+ ( )= / Save & Grade Save only
Q2. Consider the plane P C R3 given by the equation 2z-y+2z 7 and the point v2 (a) Show that the point p-5lies in P and calculate the distance between p and v (b) Find the point qE P that lies closest to v (c) What is the distance of v to P? (d) What is the angle between the vectors v - q and p -q? (e) Does the pythagoras theorem apply to the triangle formed by the points...
Question 1 1. Given the equation 3x + 4y = 5, answer the following two parts for 5 points each. a. Is the slope of the line positive or negative? b. Using any point (x, y), as x increases in value, describe the value change in y.
5. (a) Show that the point Q(1,0,0) lies in the plane x + y + z = 1 and the point P(1, -2,4) does not. (b) Find both the scalar and vector projections of the vector PQ onto the vector a = (1,1,1). (c) Use the scalar projection in (b) to find the distance from the point P(1, -2, 4) to the plane x+y+z=1.
Clara consumes two goods x and y. Suppose her utility function is given as U(x,y)=min{3x,4y} The prices of the two goods are Px for good x and Py for good y. If her monthly income is $M, Derive her uncompensated demand function for good x Derive her uncompensated demand function for good y Derive the cross-price effects and show that the two goods are complementary goods.
Q2. Consider the plane P C R3 given by the equation 2z-y+2z 7 and the point v2 (a) Show that the point p-5lies in P and calculate the distance between p and v (b) Find the point qE P that lies closest to v (c) What is the distance of v to P? (d) What is the angle between the vectors v - q and p -q? (e) Does the pythagoras theorem apply to the triangle formed by the points...
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z = z X = e e5t, y 2 + cos(7t). as X. dw A) Use the chain rule to find as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e e5t d dw 5/y(e^5t)+-x/y^2+1/z(2cos(2t))+(-y/3^2)*(-7sin(7t)) dt Note: You may want to use exp() for the exponential function. Your answer should be...