4. Consider the points P(1,0,1), Q(-2, 1, 4), R(7,2, 7). (a) Write the linear equation for...
Consider the points P(2, 1, 1) and Q(3, 0, 0). (a) Write the equation of the line that passes through the points P and Q. Express your answer with both parametric equations and symmetric equations. (b) Write the equation of the plane (in terms of x, y, z) that passes through the point P and is perpendicular to the line from part (a).
1. Consider the points A(4,0,0), B(0,3,0),C(0,0,5), and P(1,2,8). a. Write the equation of the plane passing through the points A, B, and C. b. Write parametric equations of a line passing through point P and orthogonal to the plane described in part a. c. Find the exact distance between point and the plane described in part a.
Q6 Equation 10 Points Consider the points P = (1,2,3), Q = (4,5,6), and R = (7,8,9). Decide if these points generate a plane, if so give an equation for it. Otherwise, give a set of parametric equations for the line the define. Please select file(s) Select file(s)
2. In R3 you are given the points P(0,0, 10) and Q(42, 70, 4), and R(42, 70,-4) (a) Find the equation of the linear motion which travels through P at time 0 and through R at time 7 (b) Describe the motion of the particle which travels via linear motion, passing through P at time 0, then bounces off of the ry-plane and continues via a linear motion, until it passes though Q at time 14. (Draw a sketch of...
I need some help with this problem, please. Problem 1 Consider the points P = (01,02) and Q = (U1, U2), and assume that none of 01, 02, u and uz is zero. (a) Find the slope my through O and P and the slope m2 through O and Q. (b) Let T O P, 7=and let 7.7 denote their inner product. Show that mim2 = -1 if and only if 7.7 = 0. (c) Use part (b) to explain...
Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r, y.3)r In:+sin(y:)- 0 at p. Then L intersects the plane :-0 at the point
Let L1 be the line passing through thr points Q1=(-4,-5,-2) and Q2=(0,-7,2). Find a value of k so the line L2 passing through the point P1=(7,-9,k) with direction vector d=[-1,-1,0]^t intersects with L1 K=?? Question 2 [10 points) Let Ly be the line passing through the points Or.-5. 2) and Q-0-72) Find a value of k so the line passing through the point Ps-P;(7.-9. k) with direction vector i/-/-1,-1.0" intersects with L ko
Q = (0,6, -4) R= (5,-4, -5) Consider the triangle with vertices: P= (-2,0, -1) (a) Find the vectors PO, PŘ, and QŘ (b) What is the measure of the angle at P (ZQPR)? (c) What is the perimeter of the triangle APQR ? (d) What is the area of the triangle APQR? (e) Find a vector that is perpendicular to the plane containing P, Q, and R Verify that the vector you have found is perpendicular to PO (f)...
Consider the points: P (-1,0, -1), Q (0,1,1), and R(-1,-1,0). 1.) Compute PQ and PR. 2.) Using the vectors computed above, find the equation of the plane containing the points P, Q, and R. Write it in standard form. 3.) Find the angle between the plane you just computed, and the plane given by: 2+y+z=122 Leave your answer in the form of an inverse trigonometric function.
Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric vector equation of the plane which passes through these three [3 marks] b) Find the vector cartesian equation of the plane passing through the three points listed [2 marks] c) Hence, or otherwise, find the non-vector cartesian equation of the plane passing through 3 marks] points above. the points above. Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric...