(1 point) Give a vector parametric equation for the line that passes through the point (1,...
(1 point) Give a vector parametric equation for the line through the point (0, -3, -3) that is parallel to the line (4 + 4t, -4 – t, t – 3): L(t) =
(1) (a) Find the equation of the line, Li, which passes through the points A : (4,y,z) = (0, -5, -3) and B : (x, y, z)=(3, 1,0). (b) Find the equation of the line, Ly, which passes through the points C:(x, y, z)=(-1, -3,2) and D: (x,y,z) = (4,3,6). (c) Show that L and Ly are not parallel lines. (d) Write the parametric equations for L, and L2, and then show that the lines Li and L2 do not...
Equations of Lines For problems 3 & 4 give the vector and parametric form of the equation of given line. *4. The line that passes through (10,-8, 14) and is parallel to r(t)=(9,-3+6t, 141).
(1 pt) Find a vector equation for the line through the point P = (1, -2, 3) and parallel to the vector v = (-3, 2, -3). Assume r(0) = li – 2 + 3k and that v is the velocity vector of the line.. r(t) = i + j+ Rewrite this in terms of the parametric equations for the line. X < N
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
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...
Find the equation of the line that passes through the point (2,3,4) and is perpendicular to the plane 2x-y + 3z = 4 a. x=4+2t , y=2-t, z=7-3t b. x=2+2t , y=3-t, z=4+t c. x=2-2t , y=-3+t, z=4-3t d. x=-2+4t , y=5-2t, z=-2+6t e. another solution
1. Find the vector equation of the line (a) through the point (1, 3) with gradient 2, (b) through the points (3,-5) and (-2, 4), (c) * through the point (2,-1) and parallel to the line r. (41 – 3j) – 2 = 0, (d) through the point (-3,6) and perpendicular to the line 3x - 5y = 7
8. Give the equation of a line that passes through (-1.2) and is parallel to the line defined by y-3x = 4.
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?