2. Determine a vector that is perpendicular to both a=(5,3,-1) and 5=(4,- 2.7). Show that your...
(1 point) Find a non-zero vector x perpendicular to the vectors ✓ : 2 and ū -4 -2 =
Show that the vector x = (1, 2) and the vector y = (3, 5) a base of form and determine all representations of z = (4, 7) related to the base
show all work to determine which one is a solution 2x+y>=10 y<x/2+1 a). (5,3) b). (-2,14) c). (-3,-1)
5. Find the vector 5 that is parallel to vector a = 27 -7 and has the length of 5. 6. Find the distance between two points (-1,-3,6) and (0,3,0). 7. Find the distance from the point (-5,3,-2) to a. the origin b. the x-axis c. the xz-plane 8. Let P; be the midpoint of the line segment between P.(-3,4,1) and P2(-5,8,3). Find the coordinate of the midpoint between P, and P3. 9. Knowing = (2,-3,1), 7 = (-2,0,5), and...
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...
#2 show work 2. (5 points) Find a vector of length 3 that is perpendicular to the line given by -3x + 7y = 11. Express the result in terms of the unit vectors i and j. 3. (10 points) A truck is parked on a driveway inclined 19° to the horizontal. A force of magni- tude 920 pounds is required to keep the truck from rolling down the driveway. a. Find the vector representing this force and express it...
13 2. Find a vector i of length 3 in the direction of a = [1,2,3]. 3. Consider the vectors th=[k, 2, -11) and (a) ū and are perpendicular. [3] (8.k, 1). Find the possible values of k such that: (b) u and ū are parallel. Sand ğ vectors in Rº such that P+q1l = 2 and P-911 = 3. Find p.7.
(6 points) Are the following statements true or false? 1. fi (a, b) is parallel to u 2.If iü is a unit vector, then fila, b) is a vector ? 3. Suppose f(a, b) and f(a, b) both exist. Then there is always a direction in which the rate of change of f at (a, b) is zero ?4.I f(x, y) has f. (a, b) 0 and f,(a, b) 0at the point (a, b), then f is constant everywhere |...
Determine the components of vector ?⃗ given ? = 2.5 and ?? = 50°. Show your work 3:25 PM Tue Jan 22 Math Prep HW.pdf 祺. 」 」 3. Determine the components of vector A given A 2.5 and 0A-50°. Show your work. 4. Given A 5.0, A-45°, B-3.0, B-270°, determine the magnitude and direction of vector C given C - A + B. Show your work. - soV6 0,65 Cos (415) 5O X Co 1-2 of 2 CO Dashboard...
Exercise 1. Let v = 2 ER3. Recall that the transposed vector u is ū written in row form, 3 that is, of = [1 2 3]. It can be seen as a 1 x 3 matrix. For every vector R3, set f(w) = 1 WER. (i) Show that f: R3 → R defines a linear transformation. (ii) Show that f(ū) > 0. (iii) What are the vectors we R3 such that f(w) = 0?