Given vectors a (2,-1,5), b (4,3,-2) & c (5,4,0), find: ? a) 4a - 3b + 2c b) find magnitude of vector b c) find vector of length 7 parallel to vector c

A) 4a - 3b + 2c

4(2, -1, 5) - 3(4, 3 , -2) + 2(5, 4, 0) = (8, -4, 20) - (12, 9, - 6) + (10, 8, 0) =

= (8 - 12 + 10 , -4 - 9 + 8 , 20 + 6 + 0) = (6, - 5, 26)

(6, - 5, 26)

b) magnitude of vector b



c) vector of length 7 parallel to vector c

=> m(5,4,0) = (5m,4m,0)

=>   

=> m = 7 / √41 ≈ 1.093

=> 1.093 (5, 4, 0) = (5.465 , 4.372, 0)

(5.465 , 4.372 , 0)

Letter c i’d say

A’b’c’ are the coordinates to the new location of the transformed triangle abc. find the distance between the coordinates points to use for your calculations.