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- We mentioned in Section 7.5 that our algebraic treatment of vectors could be attributed, in part, to the Irish mathematician William Rowan Hamilton. Hamilton considered his greatest achievement to be the discovery of qualernions, which he (incorrectly) predicted would revolutionize physics. Research the subject of quaternions. What are they? Why did quaternions fail to be as useful for physics as Hamilton predicted? How are quaternions useful, instead, for 3.D computer graphics? Write a paragraph or two about your findings.If u = < 3 , 9 > and v = < -3, 1 >, find 1/3u - 2v. (this is a vector problem)In Problems 21–26, decompose v into two vectors v1 and v2 , where v1 is parallel to w, and v2 is orthogonal to w. 25. v = 3i + j, w = - 2i - j
- In Problem ,use the vectors in the figure at the right to graph each of the following vectors. u - vIn Problems 23–25, use the vectors u = 2i - 3j + k andv = - i + 3j + 2k.23. Find u * v.24. Find the direction angles for u.25. Find the area of the parallelogram that has u and v asadjacent sides.I have the following vectors, I have a problem with understanding why one becomes 'a+b' and the other 'b-a' and visualising it.
- In Problems 40–45, use the vectors v = 3i + j - 2k and w = - 3i + 2j - k to find each expression. 40. 4v - 3w 41. || v - w || 42. || v || - || w || 43. v * w 44. v . (v * w) 45. Find a unit vector orthogonal to both v and w.Problem 2: Let v=⟨3,4,5⟩. Find a unit vector in the same direction as ?. ⟨_____,_____ ,____ ⟩In Problem,the vector v has initial point P and terminal point Q.Write v in the form that is,find its position vector. P =(1, 0); Q =(0, 1)