Problem-1 (10 points): The line L through the point p(-1,0,1) is orthogonal to the surface S-((r,...
1. (10) Let l be the line in 3-space that passes through the points A=(5,2, -1) and B = (6,0,–7). (a) Find a set of parametric equations for l. (b) Find the unique point P at which l intersects the plane with equation -3.21 + 722 - 2.23 = 11. (c) Let P be the point found in part (b), and let Q = (k, 7, 10) for an unspecified real number k. Determine the value of k for which...
(1 point) The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram. = So the distance from P (-4,-5, -4) to the line through the points A = (1, -2, 3) and B = (-3, 2, -3) is | (1 point) The distance d of a point P to the line through points A and B is...
5. Find parametric equations for the line through the point (0, 1,2) that is orthogonal to the line x = 1 + t, y 1-t, 2t, and intersects this line. (Hint: Try drawing this scenario in two dimensions, ie. draw two orthogonal lines and a point on each line away from the intersection. How would you find the direction vector?)
(1 point) The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram. So the distance from P = (0, 2) to the line through the points A = (-1,-1) and B=(3,0) is
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.
Question 1 (10 points] Let L be the line passing through the point P=(4, -2,5) with direction vector d=[5, 2, 2]', and let T be the plane defined by –2x-3y=z=-5. Find the point Q where L and T intersect. Q=(0,0,0)
3.(10 points) Find an equation of the tangent plane to the surface (a) z = xe” at the point P(1,0,1). (6) sin xz - 4 cos yz = 4 at the point P(11,1,1).
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...
The distance d of point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram. So the distance from P = (4,3) to the line through the points A = (-2,5) and B (-3, -5) is _______
The distance d of a point P to the line through points A and B is the length of the component of AP that is orthogonal to AB, as indicated in the diagram. So the distance from P = (-3,2,3) to the line through the points A = (2, -4, 2) and B = (0,3,-1) is _______