10. Write an equation for the plane containig the points (-7,2,1). (9.0,-2) and (-5, -1,2). Is...
Find the equation for a plane containing 3 points: A(2, 2,1) in the form: ax+by+cz+d = 0 C(0, -2,1). Put the plane equation B(3,1, 0) х — 3 z+2 = y+5 = 2 L: Find the intersection point between 2 lines whose symmetric equations are: 4 х-2 L, : у-2 = z-3 -3 Find the parametric equation for a line that is going through point A(2,4,6) and perpendicular to the plane 5х-3у+2z-4%3D0. Name: x-3y4z 10 Find the distance between 2...
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).
4. (10 points) (a) Find a parametric equation and symmetric equation of the line that pases through the point (2, -1, 3) and is parallel to the vector 7 +27 -37. (b) At what points does this line intersect the yz-plane?
4. [3/8 Points) DETAILS PREVIOUS ANSWERS SCALCCC4 9.5.013. Consider the line that passes through the point and is parallel to the given vector. (4, -3,6) < 1, 2, -3> (a) Find symmetric equations for the line. 2-6 -(x-4)= 2 3 y +3 (b) Find the points in which the line intersects the coordinate planes. (5 X IX 0) (0,9 X -6 (4 x 0, 4 X) 1 Consider the line that passes through the point and is perpendicular to the...
2. (10 points) Write the equation of the line passing through the point (2,-2) and perpendicular to the line 2x + 3y - 4= 0
(a) Find symmetric equations for the line that passes through the point (2, -2, 8) and is parallel to the vector (-1, 3,-4). -(x + 2) = 3(y-2) = -4(2 + 8). Ox+2-472.28 2-8 -4 -(x - 2) = 3(y + 2) = -4(2-8). *+2.1;2-28 (b) Find the points in which the required line in part (a) intersects the coordinate planes. point of intersection with xy-plane point of intersection with yz-plane point of intersection with xz plane
2. (20 points) Consider the point PO 2, 3) and the - 3+1 (a) Show that the point is not on the line (b) Find the shortest distance from the point to the line (e) Find the equation of the line parallel to the given line but that passes through the point P. (d) Suppose that the plane is perpendicular to the line but passes through the point P. Find the equation of the plane.
In this problem, let li be the line that passes through the points A(1,2, 4) and B(-1,3,8), and let l2 be the line with symmetric equations x +1 = 2y = 32 — 3. Parts (e) and (f) relate to the vector field F = (xy, xz, yz). (a) Show that the lines li and l2 intersect. (b) Let P be the plane that contains both lines li and lz. Find an equation for P. (c) Show that the points...
QUESTION 3 Find an equation of the plane that contains the point (1,2, -3) and the line with sym- 2 + 2 metric equations r - 2-y-1- 2 OA 3.1 +y - 23 = 11 Obrty - 23 = 9 04 4.1 – 2y – 3: = 9 00 51 + y +2 = 4 2x -y +2 = -3 QUESTION 4
In problems 1 - 4, write the equation in the slope-intercept form using the given information. 1. Write the equation in the slope-intercept form that passes through the given point and has the indicated slope m. (3,-4) and m=- 2. Write the equation in the slope-intercept form that passes through the given points: (-1,-2) and (3,-4) 3. Write the equation in the slope-intercept form of the line that passes through the point (-1, 3) and is parallel to the line...