Problem 5. Let a E R" be fixed. Suppose that vectors x, y E R" are related by the equation a = x+ (x.y)y. (a) Show that ||a||? – ||x||? 2 + ||y||? (x ·y)² (b) Deduce that ||a|| > ||x||.
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- 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 - jI would need some help with problem #46 to find the vectors T, N, and B at the given point, please?
- Can you help me find the unique vector described in problem 2?I reached this same conclusion " Tx=Ax1x2⇒Tx=0110x1x2⇒Tx=x2x1" but had difficulty explaining it in words because it is only a reflection with respect to the y=x line if there is a negative value in either the x or y original vector. eg. (-3,2) => (2,-3) reflects across the x and y axis however if both values of x,y are negative of positive the values stay in the same quadrant and the reflection occurs over a corresponding diagonal midline. As far as I can tell, the values are transpose vectors of one another, but transpose is not a linear transformation. I know I must be confusing some theorem or missing something, but I cannot find it. Is there something I am misinterpretting? Sometimes online classes are extra difficult when asking for clarification isn't immediate or easy, so sorry for the needed follow up.Solve the problem. 1. Find the symmetric equations for the line through the point P(5, -3, -5) parallel to ther vector -6i +7j -7k.
- - It is a vectors problem - Simple solutions would be better, not too advanced Question: For what values of k will the line (x,y,z) = (k,-4,-6) + t(3,2,1) intersect the plane x - 4y +5z + 5 = 0 a) in a single point? b) in an infinite number of points? c) in no points?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 + kIn Problem,write the vector v in the form ai +bj , given its magnitude ||v|| and the angle it makes with the positive x-axis.