I need some help with this problem, please.
I need some help with this problem, please. Problem 1 Consider the points P = (01,02)...
1. Consider the points A(4,0,0), B(0,3,0),C(0,0,5), and P(1,2,8). a. Write the equation of the plane passing through the points A, B, and C. b. Write parametric equations of a line passing through point P and orthogonal to the plane described in part a. c. Find the exact distance between point and the plane described in part a.
Problem 3 Consider the lines ti(t) = (1,0,–2)t + (1, -3, 2) and (t) = (0,1, -1)t + (2,0,1). (a) Find their direction vectors vị and v2. (b) Are the given lines parallel? Are they orthogonal? Explain your answers. (c) Find a parametric equation for the plane spanned by vị and V2. vers (d) Find a vector that is perpendicular to both vì and v2. (e) Find a Cartesian equation of the plane containing Vị and vŻ and passing through...
4. Consider the points P(1,0,1), Q(-2, 1, 4), R(7,2, 7). (a) Write the linear equation for the plane through P, Q, and R. (b) Write parametric equations for the line passing through P and Q.
2. Let v= [6, 1, 2], w = [5,0, 3), and P= (9, -7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be the line in R3 that passes through the point P and is perpendicular to both of the vectors v and w. Find an equation for the line L in vector form. (iii) Find parametric equations for the line L.
I need help with question 2b and 3. Please help it would be awesome if i knew how to do these questions. v=(2,-4) w=-3i+2j 2. Let and ui be as in Problem 1. Find the following quantitics (a) 2u) (ui-2t). (b) The angle between the vectors (2u) and (wi-2) 3. Let be the line defined by 2r +3y 1. (a) Find an equation of the line parallel to I, running through the origin. (c) Find an equation of the line...
1. (10) Let l be the line in 3-space that passes through the points A=(5,2, -1) and B = (6,0,–7). (a) Find a set of parametric equations for l. (b) Find the unique point P at which l intersects the plane with equation -3.21 + 722 - 2.23 = 11. (c) Let P be the point found in part (b), and let Q = (k, 7, 10) for an unspecified real number k. Determine the value of k for which...
Consider the points P(2, 1, 1) and Q(3, 0, 0). (a) Write the equation of the line that passes through the points P and Q. Express your answer with both parametric equations and symmetric equations. (b) Write the equation of the plane (in terms of x, y, z) that passes through the point P and is perpendicular to the line from part (a).
1. Let Q = (-3.-3.-3.3), R = (-3.-3,-33) and S = (1,10,10.1). In the following, when rounding numbers, round to 4 decimal places. (i) Find QR and RS. (ii) Find the angle in degrees between QR and RS. (iii) Find ||QŘ|| and ||RŠI. (iv) Find the projection of R$ onto QR. 2. Let v = [6, 1, 2], w = [5,0,3), and P = (9,-7,31). (i) Find a vector u orthogonal to both v and w. (ii) Let L be...
5. (a) Let u 1,4,2), ,1,0). Find the orthogonal projection of u on v (b) Letu ,1,0), u(0,1,1), (10,1). Find scalars c,,s such that 6. (a) Find the area of the triangle with vertices , (2,0,1), (3, 1,2). Find a vector orthogonal to the plane of the triangle. (b)) Find the distance between the point (1,5) and the line 2r -5y1 (i) Find the equation of the plane containing the points (1,2, 1), (2,1, 1), (1, 1,2). 7. (a) Let...
1. Let Q = (-3, -3, -3.3), R = (-3, -3, -33) and S = (1, 10, 10.1). In the following, when rounding numbers, round to 4 decimal places. (i) Find QŘ and RS. (ii) Find ||QR|| and ||RŠI. (iii) Find the angle in degrees between QR and RS. (iv) Find the projection of RŠ onto QŘ. 2. Let v= [6, 1, 2], w = [5,0,3], and P = (9, -7,31). (i) Find a vector u orthogonal to both v...