Either find the coordinates of the vector relative to basis B, or find the original vector from the coordinates relative to basis B. (a) v = (3,5,10); B = {(1,0,−1), (2, 1, −1), (-2, 1,4)} for R³. (b) v (13,54); B = {(1,0), (0, 1)} for R². = (c) [v]B = (10,-1, 4); B = {(1,0,−1), (2, 1, −1), (−2, 1,4)} for R³.

7. (a) Let v be a vector with initial point (-1, 4) and terminal point (3, -2). Let w be a vector with initial point (-2, -2) and terminal point (6, 7). (i) Express v and w in component form. (ii) Find the angle (in degrees) between the two vectors. (iii) Find the vectors v+w and 2v – w. -

Let the following vectors be in R³ a = (1,3,-1) b= (-2,1,3) c = (3,2,1) d = (1,-1,2) 14.- Perform the cross product of the following vectors: (a²* 3b) = (d² * 3a) =

Find two vectors Vy and V2 whose sum is (-5, –3), where 7y is parallel to (2, 5) while Uz is perpendicular to (2, 5).