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.)
Find the line through (9, 1, −6) that intersects and is perpendicular to the line x = −1 + t, y =...
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
-13 POINTS MY NOT - 10t. The (x(1), y(t)) graph intersects itself at (10,0). Find the values of t for which this intersection occurs. (Enter your answers as a comma- Consider X(t) = 12 and y(t) = separated list.) Find the two tangent lines at the point (10,0). (smaller slope) (larger slope)
Let L be the line with parametric equations x=-5 y=-6- z=9-t Find the vector equation for a line that passes through the point P=(-3, 10, 10) and intersects L at a point that is distance 5 from the point Q=(-5, -6, 9). Note that there are two possible correct answers. Use the square root symbol 'V' where needed to give an exact value for your answer. 8 N
please answer both (12(8 pts) Find parametric equations of the line through the point (2, -1,3) and perpendicular to the line with parametric equations 1-t,y 4- 2t and 3+ t and perpendicular to the line with parametric equations 3+t,y 2-t and z 3+2t. (13)(8 pts) Find the unit tangent vector (T(t) for the vector function r(t) - costi+3t j+ 2sin 2t k at the point where t 0 (12(8 pts) Find parametric equations of the line through the point (2,...
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?)
Find the point at which the line with the parametric equations x-1-1, y=1+1, z intersects the plane with the equation X-y +3.2-4.
7. (-/1 Points) DETAILS LARCALC11 11.R.037. Find sets of parametric equations and symmetric equations of the line that passes through the two points. (For the line, write the direction numbers as integers.) (7, 0,5), (10, 11, 9) (a) Find sets of parametric equations. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) (b) Find sets of symmetric equations. *57 - 11 3+5 0 - 7x + 3 = 11y = -5z +...
(a) Find symmetric equations for the line that passes through the point (4, -2, 6) and is parallel to the vector (-1, 3, -4) x+ 4-Y+ 2 3 z-6 -4 -(x +4) 3(y 2)-4(z +6). y+2 z-6 3 -(x-4) 3(y +2) -4(z- 6). o4-2-116 = Y - 2-z+6 3 (b) Find the points in which the required line in part (a) intersects the coordinate planes. 5 ,5,0 x ) point of intersection with xy-plane 10 7 point of intersection with...
Find sets of parametric equations and symmetric equations of the line that passes through the two points (if possible). (For each line, write the direction numbers as integers.) (5. -3, -2). (a) parametric equations (Enter your answers as a comma-separated list.) (b) symmetric equations XY 2+2 17 9 5-x 17 11 x-5 y - 3 15 11 2+2 9 5- X 17 Y = 2+2 9 Find f and fu, and evaluate each at the given point. y! f(x, y)...
intersects the plane Q3: Find the point where the line x x = + 2t , y = -2t, z = 1+t through P (1,1,-1). Q(2,0.2) and S (0,2,1) ?