(a) Find a unit vector that is orthogonal to the plane through the points P(0,0,–3), Q(4,2,0),...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
Please do the parts in the given order tyā (x,y)メ(0,0) (x,y)= (0,0). if if 1 (d) Given the unit vector u-( find the directional derivative of f(x, y) at the 리지, ,- point (to,m) = (0,0), in the direction of the vector a. (e) Find the gradient of f(x, y) at the point (zo,o) (0,0) (c) Find the equation of the tangent plane to the graph of the function z -f(x, y) at the point (x,y,z) (1,0,0). tyā (x,y)メ(0,0) (x,y)=...
PHY 323-Electromagnetic Theory Quiz # 1a Dr. Chinn 1. Two charges Q, of 3 C and Q, of 5 C are located at r,21+4j+ 3k and r 3i +5j -6k. a) Find the vector force F,z on Q, due to Q, in terms of unit vectors I, j, and k b) Extract the x, y and z components of force c) Find the unit vector in the direction of the force Fi2 d) Find the direction angles 12.
PHY 323-Electromagnetic Theory Quiz # 1a Dr. Chin 1. Two charges Q, of 3 C and Q, of 5 C are located at r 21+4j+ 3k and r- 3i +5j-6k. a) Find the vector force F1z on Qs due to Q2 in terms of unit vectors I, j, and k b) Extract the x, y and z components of force c) Find the unit vector in the direction of the force Fs d) Find the direction angles
please answer all qustion on expination needed 1 Find a vector of magnitude 3 in the direction of v=5 i - 12 k The vector is i+i+k (Simplify your answer. Use integers or fractions for any numbers in the expression) 2 Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations x2 + y2 +(2+152 = 169, z= - 3 Choose the correct description O A. The line through (5,0. -...
Q2. Let u and v be non-parallel vectors in Rn and define Suv (a) Does the point r lie on the straight line through q with direction vector p? (b) Does the point s lie on the straight line through q with direction vector p? (c) Prove that the vectors s and p -r are parallel. (d) Find the intersection point of the line {q+λ p | λ E R} and the line through the points u and v. Q3....
4. Let F(x,y) - PiQj be a smooth plane vector field defined for (x,y) f (0,0), and F - dr for integer j, and all suppose Q - Py for (z, y) (0,0). In the following L-JF dr for integer j, and all G are positively oriented circles. Suppose h = π where G is the circle x2 + y2-1. (a) Find 12 for G : (x-2)2 + y-1. Explain briefly. (b) Find Is for Cs: ( -2)y 9. Explain...
26 or 28 or both 25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of which is projyu. Insum of two orthogonal vect as a sum of two 26. (3.-7),2, 6) 27, u(8, 5), v 28, 2, 8), v-(9,-3 29 and 30, find the interior angles of the triangle with 25 28, find the vector projection of u onto v. Then write u In ExcTe wo orthogonal vectors, one of...
Find the three angles of the triangle with the given vertices: P(1,1,1), Q(1,−5,2), and R(−2,2,6) Find a nonzero vector orthogonal to the plane through the points: A=(0,1,−1), B=(0,6,−5), C=(4,−3,−4)
in the direction of the vector OR. Put your answer in the Given the points P 2.3.1). Q (-1.1.2) and R (1.1.0) a) (3 pts) find an equation for the line that passes through the point form r(t) = (x(t), y(t), z(t)). b) (4 pts) find a non-zero vector normal to both Po and QR c) (3 pts) find an equation for the plane containing the points P Q and R. Put your answer in the form ax+by+cz =d.