Which one of the following is a normal vector for the plane through the point P(1.-3...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
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.
The equation of the plane which is normal to the vector m=< -5, 11,8 > and contains the point P(4, 2, -1) is: a. 5x-1 ly-8z=6 b. -5x+11y+87=5 C. 4x+2y-z=-6 d. None of the above. The exact value of the position vector - [] that is formed when the initial position vector 01 = 4] is first rotated 45° in an anti-clockwise direction and then stretched by a factor of 3 is: a. Sale Sale b. = C. 61 =...
Linear Algebra Problem 4: Given the normal vector n - 2 determine the matrix of the projection linear map through the plane (passing through the origin) which has n as a normal vector. Problem 5: Given the normal vector n = linear map through the plane (passing through the origin) which has n as a normal vector. V14' V14 V14 (#าพื้าพื้) determine the matrix of the reflection V14' V14 v14 Problem 4: Given the normal vector n - 2 determine...
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
(a) Find a unit vector that is orthogonal to the plane through the points P(0,0,–3), Q(4,2,0), and R(3,3,1) (b) Find two non-parallel vectors that are orthogonal to the vector Ŭ = i + 2) + 3k (c) Find the angel between the vector Ở = 51 + 21 – k and the z - axis (d) Describe why it is impossible for a vector to have the following direction angles 511 6 -, B = 3, and y TT π...
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...
(1 point) Find the derivative of the vector function r(t) = ta x (b + tc), where a= (4,3,-4), b = (2,1,2), and c = (5,-1,3). r'(t) = {
(1 point) (A) Find the parametric equations for the line through the point P = (-4, 4, 3) that is perpendicular to the plane 4.0 - 4y - 4x=1. Use "t" as your variable, t = 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. (B) At what point Q does this line intersect the yz-plane? Q=(