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4.[10 point] Parametrize the plane through the points (1,0,0), (0, 2, 0), and (0, 0, 3).
5,6 please
5. Parametrize the plane P in R3 containing the points x (1,0, ), x (2,0, 1) and x3 (1,3, 1). Does the plane P contain the point (-1,3,2)? 6. Sketch and parametrize the triangle in the plane with vertices x! = (-1,-2), x2 = (2, and x3 (1,3). Does this triangle contain the origin (0, 0,0)
16. [3 points]Write the equation of the plane that passes through the point (0, 2, -1) and contains the line given by x = 2y = 2-3 slo bus dt of boilqqa od ot batin pt 911 di 10 abusingsmorit ei tedatnioq El.AI Cmos lo uprot soubora od 2€ lo algne as te donarw 11-1
5. (a) Show that the point Q(1,0,0) lies in the plane x + y + z = 1 and the point P(1, -2,4) does not. (b) Find both the scalar and vector projections of the vector PQ onto the vector a = (1,1,1). (c) Use the scalar projection in (b) to find the distance from the point P(1, -2, 4) to the plane x+y+z=1.
Find a point-normal equation of the plane passing through points A(1,-1,0), B(0, 0, 2) and C(0,3,1).
--1)+3y+2(z-4) 0 (9) Find an equation of the plane (a) through the point (2,0, 1) and perperndicular to the line a =3t, y 2- t,z3t+4 (b) passes through the point (1,-1,-1) parallel t the plane bz-y-z6 (c) passes through the point (3,5,-1) and contains the line a 4-t,y = -1+2t, z3t (d) passing through (-1,1,1), (0,0,2) and (3,-1,-2).
Find an equation of the plane. The plane through the point (3, 0, 1) and perpendicular to the line x = 6t, y = 2 − t, z = 9 + 4t
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?
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
Find an equation of the plane passing through the given points. (3, 4, –4), (3, -4,4), (-3, -4, -4) Tx - 69 - 7z - 25 = 0 x
2. (5 points) (a) Find a vector perpendicular to the plane through the points A(0, -2,0), B(4,1, -2) and C(5,3,1). (b) Find an equation of the plane through the points A, B, and C. (b) Find the area of the triangle ABC.