10. Express the following in vector form: a. Line IcR that passes through the points A-(-1,-1,0)...
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...
(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...
Find the normal form of the equation of the plane that passes through Find the vector form of the equation of the line in ℝ2 that passes through P = (5, −2) and is parallel to the line with general equation 5x − 4y = 2.
Q4. (5 points). Find the equation of the plane that passes through the line of intersection of the two planes x - 2y = 3 and y- z = 0 and parallel to the line x = y - 1 = 2+1 Q5. (4 points). Find the distance from the point A(1,2,3) and the line 2+1 y-1 2 Q6. (4 points). Give the name and sketch the surface whose equation is given by x2 + 2y2 – 12y – z...
Find the equation of the plane that passes through the ine of intersection of planes x+z=1 and y+2z=3 and is orthogonal to the plane x+y+z=34256. Express your answer in general form.
Problem 4: (a) (5 points) Find the equation for the line that passes through the points (-4,-2) and (8, 1). Write your equation in se form, slope-intercept form, or point- slope form. (Extra Credit: Write the equation for the line in all three forms) (b) (5 points) Graph the line. Problem 5: (10 points) Find the equation for the line passing through the point (3.2) and perpendicular to the line y = ',x + 7. The the line Problem 6:...
In this problem, let li be the line that passes through the points A(1,2, 4) and B(-1,3,8), and let l2 be the line with symmetric equations x +1 = 2y = 32 — 3. Parts (e) and (f) relate to the vector field F = (xy, xz, yz). (a) Show that the lines li and l2 intersect. (b) Let P be the plane that contains both lines li and lz. Find an equation for P. (c) Show that the points...
Find the slope-intercept form of the equation of the line that passes through the points 6,9) and (-8,-7), and find the x-intercept. Equation of the line in slope-intercept form: y- x-coordinate of x-intercept Enter an integer or fraction.)
in the direction of the vector OR. Put your answer in the Given the points P 2.3.1). Q (-1.1.2) and R (1.1.0) a) (3 pts) find an equation for the line that passes through the point form r(t) = (x(t), y(t), z(t)). b) (4 pts) find a non-zero vector normal to both Po and QR c) (3 pts) find an equation for the plane containing the points P Q and R. Put your answer in the form ax+by+cz =d.
Find the general equation and a vector equation of the plane that passes through the points p(1,2,4) Q(1,-1,6) R(1,4,8)