4. For the vectors b = (1, 2, −2) and a = (−3, 0, 4) (a) Compute the projection of vector b onto the line along vector a as p = ˆxa. (b) Compute the projection of vector b onto the line along vector a as p = Pb. (c) Compute the error vector. (d) Compute the length of the projection vector and length of the error vector.

a) and b) p= (33/25, 0, -44/25)

c) e = (-8/25, 2, -6/25)

d) p = 11/5 = 2.2

e) e = (2/5)√26 = 2.039

Step-by-step explanation:

Given

b = (1, 2, −2)

a = (−3, 0, 4)

a)  and b) We use the formula

p = (at*b)/(at*a)*a

⇒ p = ((−3, 0, 4)*(1, 2, −2)/((−3, 0, 4)*(−3, 0, 4)))*(−3, 0, 4)

c)

d) We use the formula

e) Applying the same formula we have

the surface area is 124cm²

step-by-step explanation:

length: 4cm

width: 9cm

height:   2cm