Consider the three points: A = (8,7) B = (1,5) C = (5,1). Determine the angle...
Consider the three points: ?=(5,7) ?=(2,3) ?=(7,1). Determine the angle between ??⎯⎯⎯⎯⎯⎯⎯⎯ and ??⎯⎯⎯⎯⎯⎯⎯⎯.
Part c and d Question 5 (30 marks) Let A1, B(3,-5,0) and C(-1,4,1) be three points in R. Use vector method(s) to solve each of the following. R-8 (a) Find the unit vector u in the direction of AB-3AC. (b) Calculate the smaller angle betwen AB and AC. Correct the answer to ONE decimal place. (c) Find the shortest distance between B and the line passing through A and C. Correct the answer to ONE decimal place. (Hint: Consider the...
Let A-B-C denote B is between A and C. For this problem, use the following three axioms: A1: Each pair of points is assigned a number, called the distance between A and B. it is denoted by AB. A2: Given any points A and B, then AB 20. Equality holds precisely when A=B. A3: For all points A and B, ABEBA Suppose A, B, C, and D are collinear. Assume that A-B-C means: A, B, and C are distinct, collinear...
Let A, B, and C be three collinear points s.t. A*B*C. Prove each of the follow set equalities. I'm really having trouble applying theorems like the ruler placement postulate or betweenness theorem to help prove these. 24. Let A, B, and C be three collinear points such that A * B * C. Prove each of the following set equalities. (a) BÁ U BỎ "АС (b) BA n BC {B} (c) ABU BC AC (d) AB n BC {B} (e)...
Consider the rules AB -> C, AC -> B, BC -> A, where A,B,C are three items. The support for all the 3 rules is the same. a) TRUE b) FALSE
5. Given the points A = (0,0), B = (5,1), C = (2,6) on the plane. Use a determinant to find the rea of the triangle ABC.
Be the next function , Determine in points (2, -5,1): a) Divergence of the function b) Rotational of the function G(x, y. z) (24cosxyz* )i+(10e*sinyz°)j- 2(xyz )k G(x, y. z) (24cosxyz* )i+(10e*sinyz°)j- 2(xyz )k
Given the points AC - 5,2, – 3), B( - 1, - 9,2), and CC - 4, 3, 4), find (a) the angle between AB and AC, (b) the angle between BA and BC, and (c) the angle between CA and CB. (a) ZBAC = (b) ZABC = (c) ZACB =
6. Given the points A = (0,0),B = (5,1),C = (2,6) on the plane. Use a determinant to find the area of the triangle ABC.
28 Consider (O:OAOB) an orthonormal system in space. Let G be the center of gravity of triangle ABC. 1° Calculate the coordinates of G 2°Consider the points A' (2 ;0:0) ,B, (0:2:0) and C" (0:0,3). a) Verify that these three points define a plane. b) Write a system of parametric equations of the plane (A'BC'). 3 Write a system of parametric equations of line (AC). 4° Verify that K (4:0-3) is the trace of the line (AC) with the plane...