3. LARCALC11 11.5.045. Find an equation of the plane with the given characteristics. The plane passes...
Find an equation of the plane with the given characteristics. The plane passes through (0, 0, 0), (2,0, 6), and (-3, -1, 9). Find the distance between the point and the plane. (0, 0, 0) 3x + 7y + z = 21 The position vector r describes the path of an object moving in space. Find the velocity v(t), speed s(t), and acceleration a(t), of the object. r(t) = ti + Rj+ K
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...
Question 3 a) Find the cartesian equation of the line that passes through the origin and lies perpen- (3 dicular to the plane 3x - 5y +2z 8. marks] b) Find the cartesian equation of the plane that lies perpendicular to the line 3 marks] and passes through the point 1 cExplain why a unique plane passing through the three points A(-2,-1,-4), B(0,-3,0) [2 marks) and C(2,-5,4) cannot be defined. Question 3 a) Find the cartesian equation of the line...
18. Find the equation of a plane that passes through the points (2, -2, 1), -1, 0, 3) [5 marks] and (5,-3, 4). Does the point (2, 1, -3) lie on the plane?
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 +...
Find the equation of a plane that passes through the points (2,-2,4), (1, 3,-2) and (5, 0, 1). Does the point (2, 3, -9) lie on the plane? 19. [5 marks] Assignment 2.1Bsp...pf Show All
5. Find the equation of the plane which passes through the point (6,0,-2) and contains the line x = 4-2, y = 3 + 5t, and z 7+4t.
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.
10. [-/1 Points] DETAILS LARCALC11 13.R.069. Find an equation of the tangent plane to the surface at the given point. z = x2 + y2 + 2, (1, 3, 12)
Find an equation of the plane that passes through the point (9,4,0) and contains the line x = −4−t , y = −2+6 t , z = 4+8 t