B. Distance from a point to a plane: We'll give a general formula Monday in class....
(1 pt) (A) Find the parametric equations for the line through the point P = (2, 3, 4) that is perpendicular to the plane 2x + 1 y + 3z 1 . Use 't', as your variable, t 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. X= y- (B) At what point Q does this line intersect the yz-plane?
1 point) Suppose that the line l is represented by r(t)- (12+ 2t, 23 +6t, 8 + 2t) and the plane P is represented by 2x + 4y + 52-23. 1. Find the intersection of the line & and the plane P. Write your answer as a point (a, b, c) where a, b, and c are numbers. Answer 2. Find the cosine of the angle 0 between the line l and the normal vector of the plane P Answer:...
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...
(3) On page 136 of the workbook, we developed a formula for the shortest distance from a point to a plane. To briefly recap, suppose P = (21,41, 21) is a point with corresponding position vector p, and II is a plane with normal n = (a, b, c) given by ax + by + cz = d. Then the shortest distance from P to the plane is given by p-q|l, where Q is the point (with corresponding position vector...
Use Lagrange multipliers to find the shortest distance from the point (2,0, -9) to the plane x + y + z = 1 MY NOTES ASK YOUR TEACHER 10. DETAILS SESSCALC2 11.6.049. Find parametric equations for the tangent line to the curve of Intersection of the paraboloid = x2 + y2 and the ellipsoid 3x +212 +722 - 33 at the point (-1,1,2). (Enter
3. Consider the following system of linear equations: 2x + 2y + 2kz = 2 kx + ky+z=1 2x + 3y + 7z = 4 (i) Turn the system into row echelon form. (ii) Determine which values of k give (i) a unique solution (ii) infinitely many solutions and (iii) no solutions. Show your working. 2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w....
these are the steps given to use thank you! int. What is the distance between a line that contains points A(11, -1) and B(-3, -11) and Point P(-1,1) C)Finding the distance between a line and a point. Steps 1) Find slope (m) of given the line AB. 2 Write the equation of line AB. 3Y Find the slope (m,) of the line that is WE AС perpendicular to line AB. 4Y Write the equation of the perpendicular line w using...
In each case find () the point of intersection of the line and plane, and (ii) the angle between the line and plane: line plane r"(2i +4j-k}# 28 r-I 2 3-г 2x + 3y + z = 11 (c) 4 +K 3 2x+4y-1 0
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...