2. (5 points) (a) Find a vector perpendicular to the plane through the points A(0, -2,0),...
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.
Q = (0,6, -4) R= (5,-4, -5) Consider the triangle with vertices: P= (-2,0, -1) (a) Find the vectors PO, PŘ, and QŘ (b) What is the measure of the angle at P (ZQPR)? (c) What is the perimeter of the triangle APQR ? (d) What is the area of the triangle APQR? (e) Find a vector that is perpendicular to the plane containing P, Q, and R Verify that the vector you have found is perpendicular to PO (f)...
Find the plane through the points (1,0, 0), (0, 2,0), and (0,0,4)
(41) find the equation of the plane passing through the points A(3,-2,0), B(2,0,3), and C(1,-1,1) in (i) vector form (ii) parametric form (iii) cartesian form
Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric vector equation of the plane which passes through these three [3 marks] b) Find the vector cartesian equation of the plane passing through the three points listed [2 marks] c) Hence, or otherwise, find the non-vector cartesian equation of the plane passing through 3 marks] points above. the points above. Question 4 6-69) Consider the following three points: a-0 b-3and c-1 a) Find the parametric...
Find the equation of a plane that is perpendicular to the vector 2i −2j +3k and passing through the point (3,4,−2) The plane is given by:
--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
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
Consider the points below. P(1, 0, 1), ((-2, 1, 3), R(4, 2, 5) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR.