1. In the plane Rd let the points A(3,-2), B(4,3) and C(-2, 4) be given. Find...
2. Let P(2, 2), Q(3,5) and R(4,3) be three points in the xy plane. (a) Determine the vectors a = PO, b =PŘ, and c =RQ and draw them on the xy plane below. (b) Calculate a - b and compare it to c. What do you notice? Explanation? R 2
Q1. Given the points A: (0,0,2), B: (3,0,2), C: (1,2,1), and D: (2, 1,4 a) Find the cross product v - AB x AC. b) Find the equation of the plane P containing the triangle with vertices A, B, and C c) Find u the unit normal vector to P with direction v d) Find the component of AD over u and the angle between AD and u, then calculate the volume of the parallelepiped with edges AB, AC, AD...
2. Let A:(-1,1,-1), B:(2,0.2), C:(4.1.-3), and D:(-3, 1, 10) be points in R. (a) Find the angles (in degrees) of the triangle with vertices A, B and C. (b) Find an equation of the plane passing through the points A, B, and C. (c) Find two unit vectors perpendicular the plane through A, B, and C. (d) Find the volume of the tetrahedron with vertices A, B, C, D. 3. (a) Find an equation of the tangent line to the...
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...
The plane passing through the 3 points A(4, -2, 1), B(4, -1,4) and C(1,-4,2) can be expressed as a parametric vector equation of the form x a 1V+ 12v2 where 1 and d2 are real parameters. You are given that V1 Find suitable vectors a and V2 and enter them in the boxes below. You must enter your answers using Maple notation, for example, the vector \(\begin{pmatrix}1\2\\3\end{pmatrix} is entered as <1, 2, 3>. a = Your response Correct response No...
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 B= {[3]• [4]) and c = ( ) [1]} be two basis for R. (1) Suppose Find x, y, are these vectors equal? What does this mean geometrically? i.e. draw x and y in a plane as a linear combination of vectors in B and C. (2) Let u Find the corresponding coordinate vectors us and ſuc. What does this mean geometrically? (3) Find the change of coordinate matrix Pg and use Pg to compute us from part (2).
Let A, B, C, and D be four distinct points in the plane. Suppose that no three of them lie on a line and A, C are on opposite sides of the line BD. The lengths of the line segments AB, BC, CD and DA are 1, 2, 3 and 4 respectively. (a) What is the range of possible values for the length x of the line segment BD? You should justify your answer carefully! [5 marks] (b) Now suppose...
Moving to another question will save this response. Question 15 Q14B Given the plane P which contains the points A(3, 2, -4), B(5, 2, 1) and C(2, -3, -4). Note: Write your answers in the vector form of ai + bj + ck. a) Find the position vector AB. АВ: b) Find the position vector AC. AC = c) Find AB X AC. AB x AC = Asus AB x AC = d) Determine the parametric equations for the line...
Instructions: 2 3 -4 3 Find V Let V be the plane spanned by the vectors UT 2 0 1