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7. Let 7 = (1,-1,-2), ū = (2,-1,1) and = (2,-2,-4). Find: (a) *(-20) (4 pts)...
7. Find the angle between the vectors. ü = (-3,2) and v = (-1,1) e perpendicular. 112 - at 4. Find the vector v such that. ||3|| = 9 and having the same direction as ū. ū=(3,-2)
problem 1 and problem 2 please , thankyou very much PROBLEM 1 (25%) Find: Let: ū= (1,-1,-2) v = (-2,-2,3) w = (3,-1,1) (a) The angle between ū and w (b) Orthogonal projection of u against v (c) The area of parallelogram formed by u dan v (d) The volume of parallelpiped shaped byū, v, dan w PROBLEM 2 (15%) Determine if these sets of points are coplanar: (a) A(1,1,-3); B(0,1,-2); C(-3, 1, 1); D(2, 1, -4) (b) E(1,1,-1); F(0,1,1);...
2. Let ū= (3,1, -7), ã = (1,0,5). (a) Find the vector component of u along a. (b) Find the vector component of ü orthogonal to ä. (c) Find the angle between u and , in degrees.
8. If ū= 8î - 159 and v = -3i - 4ſ and w = 12 + 69, then find the following: A. 2w - 3ū B. ||2u - 57 C. v. W D. the angle between ü and v E. the direction angle of vector w F. (3 +70).ü G. a vector in the same direction as ū with magnitude of 12 H. a vector orthogonal to vector v with magnitude of 7 I. any vector that is orthogonal...
1. Let ū= (2,4,-1), v = (3.-3,-1) (a) Compute: x ū (b) Compute: ü x 7 (c) Is the cross product commutative? If not, what is it instead? 2. Let A = (7, -11,3), B = (1,9, -3), C = (-6,3, -2), D= (0,-8, 12), E = (1, -13,2) (a) Give the vector equation of a line passing through the points A, B. (b) Find the equation of the plane containing the points C,D,E. (c) Find the point of intersection...
(10 pts) 4/ Let f(x,y)= xet-3 and P = (1,1). a) Find the rate of change of fin the direction of Vf. Interpret the rate. b) Find the rate of change of fin the direction of a vector making an angle of 90 counterclockwise with Vfp
Let the vectors a = <1,2,3>, b= <1,1, 1 > and c = <1,2, 1 > a) Determine whether the three are coplanar None of these 4 0.71 0.74 no b) Find the volume of the parallelepiped form c) Find the unit vector orthogonal to both ved d) Find the angle between the vectors a and 22.26 bunded to 2 decimal points) 12:21 e) Find the component of the vector a along 39.51 -1 ge
1. Given the vectors ū=(1,-2,-6) and v = (0,-3,4), a) Find u 6v. b) Find a unit vector in the opposite direction to ū. c) Find (ü.v)v. d) Find 11: e) Find the distance between ū and v. f) Are ū and y parallel, perpendicular, or neither? Explain. g) Verify the Triangle Inequality for ū and ū.
006 10.0 points Find the vector ✓ with magnitude 3 and the same direction as ū= (4, -4). 1. (3,-3) wios 12' 2) 4. None of these
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...