11. Find the direction angle of 3i+ j. b. 198.430 d. 18.43° a. 25.990 c. 108.43° 12. Find the projection of u-<-6,-7> onto v = <1,1>. 91 a. 13 13 b. <39,ア 1764, 1764 c. 2 2 d. 13 13 <-13.了 ㄑㄧㄒˊ--2> 13. Find a unit vector u with the same direction as x =-40, 9>. a. 9 40 b. 40 9 41, 41 41, 41 С. 43 d. 40 9 49, 49
14. If u is a vector with magnitude of 18 and direction angle of 80º and vis a vector with magnitude of 24 and direction angle of 150°. find the magnitude and direction angle of utv. 15. If | V = 2 and 0 = 300°, write v in component form. 16. An airplane is heading north at an airspeed of 400 km/hr, but there is a wind blowing from the southwest at 60 km/hr. How many degrees off course...
14. If u is a vector with magnitude of 18 and direction angle of 80° and V is a vector with magnitude of 24 and direction angle of 150°, find the magnitude and direction angle of utv. 15. If | V2 and 9 = 300°, write V in component form. 16. An airplane is heading north at an airspeed of 400 km/hr, but there is a wind blowing from the southwest at 60 km/hr. How many degrees off course will...
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Use the vectors u = 2i - j, v = 21 - 3j, and w = -3i + 5j to evaluate the expression. 2v - u + w Find a unit vector in the same direction as the given vector. a = 201 - 21j
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...
[3] Given: u = -8i + 6 v = i- j w = 4i - 8j T = -10i Point Pat (-17, -v2), point at (-9, 11), and point Rat (8, -15) Five of the following six parts are each worth 3 points. Part b is worth 5 points. a) Find the position vector, in xi + yj form, for the vector whose initial point is R and whose terminal point is 9. b) Sketch the position vector determined by...
1. 2. Find u v and the angle between vector u and v for a) u = 2i – 2j + k, v = 3i + 4k b) u = v3i – 7j, v = v3i+j – 2k c) u = 2i +j, v= i + 2j – k
2. Given the vectors u = 2i + 3j and v = -3i - 2j (a) (4 points) Plot and label each vector (b) (4 points) Find w = u + v (c) (4 points) Find the unit vector of w
6-7. Given vectors U = -4i +12, V = 5i - 2j, W=-3i- 6. Find a) 30 - 5V._b) 2V - W'. 7. a) UW What can you tell from the result? b) angle between U and V (keep one digit after decimal. calculato
3. Consider two vectors u = 2i -j +2k and v=3i+2j-k. (a) Find a vector orthogonal to a and b. _ [3 marks] (b) Show that the vector from (a) is orthogonal to a and b. [1 mark]