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- In Problem ,use the vectors in the figure at the right to graph each of the following vectors. 3v + u - 2wIn Problems 2 to 4, find out whether the given vectors are dependent or independent; if they are dependent, find a linearly independent subset. Write each of the given vectors as a linear combination of the independent vectors.2. (1, −2, 3), (1, 1, 1), (−2, 1, −4), (3, 0, 5) 3. (0, 1, 1), (−1, 5, 3), (1, 0, 2), (2, −15, 1)4. (3, 5, −1), (1, 4, 2), (−1, 0, 5), (6, 14, 5)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
- If u = < 3 , 9 > and v = < -3, 1 >, find 1/3u - 2v. (this is a vector problem)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.In Problems 45–50, find the unit vector in the same direction as v.45. v = 5i 46. v = - 3j 47. v = 3i - 6j - 2k 48. v = - 6i + 12j + 4k 49. v = i + j + k 50. v = 2i - j + k
- In 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.In Problems 31–35, use the vectors v = - 2i + j and w = 4i - 3j to find: 31. v + w 32. 4v - 3w 33. || v || 34. || v || + || w || 35. Find a unit vector in the same direction as v.In Problem,write the vector v in the form ai +bj , given its magnitude ||v|| and the angle it makes with the positive x-axis.
- Here are three vectors in meters:d→1=-1.90î+2.70ĵ+8.80k̂d→2=-2.00î-4.00ĵ+2.00k̂d→3=2.00î+3.00ĵ+1.00k̂What results from (a) d→1⋅(d→2+d→3), (b) d→1⋅(d→2×d→3), and d→1×(d→2+d→3) ((c), (d) and (e) for î, ĵ and k̂ components respectively)?Problem 2: Let v=⟨3,4,5⟩. Find a unit vector in the same direction as ?. ⟨_____,_____ ,____ ⟩I would need some help with problem #46 to find the vectors T, N, and B at the given point, please?
