1. Let ū= (2,4,-1), v = (3.-3,-1) (a) Compute: x ū (b) Compute: ü x 7...
please anyone answer all the questions as soon please 2 4 3 3 4 1. Given three points A = (0,–8, 10), B = (2, -5, 11), C = (-4,-9, 7) in R3. (a) Show that these three points are not collinear (not in a straight line). (b) Find the area of the triangle ABC. (c) Find the scalar equation of the plane containing the points A, B and C. (d) Find a point D on the plane such that...
1. Let {ü, 7,w, i}, where u = (3,-2), v = (0,4), ū = (-1,5) and i = (-6,4). Find the components of the resultants obtained by doing the following linear combinations. a. r = 2ū - 40 b. š= 3ū – +20 +
3. If ū= 4.2,1 and ū= -2.2.1), find a vector in R3 that is orthogonal to both ū and . Answer: 4. Let A, B and C respectively denote the points (1,1,2), (-3, 2, 1) and (4, -2, -1). Find AB, AC and AB X AC. Answer: AB= AC = 1. AB X AC = 5. (a) Find the equation of the plane containing the points A, B and C above. Answer: (b) Check that your answer to (a) above...
Pl 1. Consider 3-space with the dot product. Algebraically find the projection of ū onto ü. Plot ü, ō, ūl, and ūl. (a) u = (b) u = * 0 (c) ü = U = 0
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...
Given in space the points A(4,7,1), B(2,1,3), and c(0,-1,2) The vectors ū = AB , and ✓ = AC a. (9%) Find ū. v , ū x ū , proj, u b. (3%) Find the area of triangle ABC. c. (3 %) Find the parametric equation of line (AB). d. (3 %) Find the distance from point C to the line (AB). e. (3 %) Find the equation of the plane (ABC). A relatively easy way of getting into international...
7. Let 7 = (1,-1,-2), ū = (2,-1,1) and = (2,-2,-4). Find: (a) *(-20) (4 pts) (b) (+37). ū (4 pts) (c) The vector of magnitude 5 that points in the same direction as (4 pts). (d) The angle between 7 and ū (4 pts). (e) Find Projz() (4 pts).
Question 7 (10 points] Let Ly be the line passing through the points Q1-(3,-1,-4) and Q2=(5,-3,-2) and let La be the line passing through the point P4-(12,-4, 3) with direction vector a-(-6, -6, -21". Determine whether Ly and L2 intersect. If so, find the point of intersection Q. The lines intersect at the following point Q: Q=(0,0,0)
5 3 1 Let ū = < 2,-3> V = <-2,0 > w = <3,3 > Graph vectors ū, ū, and w in standard position with corresponding terminal points, A, B, and C, respectively. (72 point) What is the length of the altitude of AABC from vertex A? (72 point) -5 -3 -1 -1 0 1 3 5 -3 -5
find the point of intersection of the line 1) Find the equation of the line passing through the points A(1,-5,-3)and B(2,-4,8) (3 marks) b) Find the equation of the plane perpendicular to the line in part (a) given that C(1,-9,6) is a point on the plane. (3 marks) c) Find the point of intersection of the line and the plane in parts (a) and (b) above respectively. (3 marks)