5 Find x and y such that is perpendicular to both (-₁) and (-1).
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- 2) Consider the two vectors à = Agî + Ayĵ and B = Bzî + Byf. If î · î = ĵ • j = 1 and î ·j = j • î = 0, prove algebraically that à · B = A,Bx + A,By.Describe all vectors in span{(3,0,2), (-2,0,3)} (so computationally what do the vectors look like?). Also give a geometric description for these vectors (what space are you in and visually what do you get? Be as descriptive as you can!).(b) Write a necessary condition for a transformation (q,p) to (Q,P) to be connonical. Prove that P-2(1+√qcosp)√q sinp:Q-log(1+√qcosp)
- Find the distance from the point (2, –7, –6) to the line L = (-5,–10, -5) + t (8,7,6) , -∞Let's consider two vectors, A = (-7, 10), B = (-5, -8), and C = (-1, 6) as shown below. A C B What is the magnitude of A+ B+ C? Answer What is the direction (8) of A+B+C relative to +x-axis? a-839 b. 20 C-85 3 d. 148°Evaluate the commutator è = [x², Pe** =?