(1 point) Consider the line L(t) = (2+ 3t, 6-t). Then L intersects: 1. The X-axis...
Problem 1. (1 point) The line x = [3t – 6,4,6 – 5t] intersects the plane 2x + y + z = 0 at the point when t = Note: You can earn partial credit on this problem.
Find the point, P, at which the line intersects the plane. x= -6 - 3t, y = -3- 9t, z= -6+ 4t: 8x + 2y +6z = 5 The point, P, at which the line intersects the plane is (00). (Simplify your answer. Type an ordered triple.)
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...
Consider line L, given below. x = 6 + t, y = 7 + t, z = 3 + 3t, tER (a) Find point P that belongs to the line and direction vector v of the line. Express v in component form. P = V = (b) Find the distance from the origin to line L.
(8 points) Find the points of intersection in R3 of the line L(t) = (3-1, -2+1, 3t) and the unit sphere: x2 + y2 + x2 = 1 (Hint: Use x = 3t - 1, y = -2t + 1 and 2 = 3t in the equation of the sphere, and solve for t.)
Find the line through (9, 1, −6) that intersects and is perpendicular to the line x = −1 + t, y = −3 + t, z = −1 + t. (HINT: If (x0, y0, z0) is the point of intersection, find its coordinates. Enter your answers as a comma-separated list of equations.)
Consider the parabola y = 7x - x2. Find the slope m of the tangent line to the parabola at the point (1, 6). using this definition: The tangent line to the curve y = f(x) at the point P(a, f(a)) is the line through P with slope m=lim x rightarrow a f(x)-f(a)/x-a provided that this limit exists. m = using this equation: m=lim h rightarrow 0 f(a+h)-f(a)/h m= Find an equation of the tangent line in part (a). y...
(1 pt) Consider the sphere (x - 4)2 + (y - 3)2 + (z - 5)2 25 (a) Does the sphere intersect each of the following planes at zero points, at one point, at two points, in a line, or in a circle? The sphere intersects the xy-plane ? The sphere intersects the xz-plane ? The sphere intersects the yz-plane ? (b) Does the sphere intersect each of the following coordinate axes at zero points, at one point, at two...
Help me solve this question asap 4 Th e centre of a circle lies on the line 3y-4x-11 and the circle intersects the y-axis at the points (0,-1) and (0,11) a) Find the equation of the circle. b) Find the possible values of λ such that the circle passes through the point 4 marks] 2 marks] c) Find the coordinates of the points where the circle meets the line y-x-11-0 [4 marks] 4 Th e centre of a circle lies...
Find the line through (3, 1,-2) that intersects and is perpendicular to the line x =-1 + t, y =-2 + t, z =-1 + t. answers as a comma-separated list of equations.) x=-1+3, y = -1, z = 31-2 X We were unable to transcribe this image