Question

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

Answer 1

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)

Answer: (6, - 5, 26)

b) magnitude of vector b


`√(4^2+3^2+(-2)^2) = √(16+9+4) = √(29) ~ 5.4`

c) vector of length 7 parallel to vector c

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

=>
`√((5m)^2+(4m)^2+0)= √(25m^2+16m^2)= √(41m^2)=m √(41)=7`

=> m = 7 / √41 ≈ 1.093

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

Answer: (5.465 , 4.372 , 0)