Q6 Equation 10 Points Consider the points P = (1,2,3), Q = (4,5,6), and R =...
4. Consider the points P(1,0,1), Q(-2, 1, 4), R(7,2, 7). (a) Write the linear equation for the plane through P, Q, and R. (b) Write parametric equations for the line passing through P and Q.
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).
3. (5 points) Consider the points P(1,2,3), ((3,0,4) and R(4.-2,3). a Find area of the triangle created by P, Q, and R. b. Find the equation of the plane containing the points P, Q, and R.
5.) Find the equation for the plane containing the points P (5,1,4), 0 (5.312), R (1,-2,2) -- 6.) Build a parametric equations for the line tangent to the curve r(t) = 572; +(6+1); - +3K at the point P (20.-11,8)
7) Consider the surface S: x2 +y2 - z2 = 25 a) Find the equations of the tangent plane and the normal line to s at the point P(5,5,5) Write the plane equation of the plane in the form ax + By + y2 + 8 = 0 and give both the parametric equation and the symmetric equation of the normal line. b) Is there another point on the surface S where the tangent plane is parallel to the tangent...
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.
Q1 A Plane in 4-Dimensional Space 50 Points Consider the plane P ER* described by the system of equations. x1 + x3 + x4 22 + 2x3 + 3x4 = = 0 0 Q1.1 The Plane as a Kernel 25 Points Express the plane P as the kernel of some matrix, that is P = ker(A1) (always show your work/explain your thinking) Please select file(s) Select file(s) Submit Answer Q1.2 The Plane as an Image 25 Points Express the plane...
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)...
I cannot get i) or j)
3. (20 marks) Consider the parallel lines L, : x= -3 +8 2 [1] and L2: x = 0 + [2] 4. and 11 [3 -21 the planes P1 : 3x + 2y + 2z = -7 and P2 : 2.x – 2y - 2 = 11. (a) Find the equation of a plane in standard form containing both L, and L. (b) Find an equation of the line of intersection of P, and...
Problem 1. (33 Points) (a) Consider the following: Are these two planes parallel? If not, find the parametric equation of their line of intersection (b) Describe the set of all points P = (x, y, z) such that the distance from P to the y-axis is twice the distance from P to the zz-plane. (c) Describe the set of all points P (r, y, 2) such that the distance from P to the plane x + 5y-4z = 1 equals...