Linear algebra. Do both part i and part ii. I have found part i and wanted to check my work. Part ii im severly confused about. 3. Let a= | 3 (i) Compute the perpendicular projection of the vector b1on the line in the direction 2 of a. (ii) Write a formula for the distance of the point Xa to the point b. Show that this distance attains the minimum value when a_ p is the perpendicular projection found in (i). Solution Projection of b in the direction of a=(a dot b) =(1 3 -2) dot (0 1 2) =(1*0)+(3*1)+(-2*2) =0+3-4 =-1 a dot a=(1^2)+(3^2)+(-2^2) =1+9+4 =14 now [(a dot b)/a dot a]=-1/14 now {[(a dot b)/a dot a]}b=(-1/14)(0, 1, 2) =(0,-1/14,-2/14).

1. Linear algebra. Do both part i and part ii. I have found part i and wanted to check my work. Part
ii im severly confused about. 3. Let a= | 3 (i) Compute the perpendicular projection of the vector
b1on the line in the direction 2 of a. (ii) Write a formula for the distance of the point Xa to the
point b. Show that this distance attains the minimum value when a_ p is the perpendicular
projection found in (i).
Solution
Projection of b in the direction of a=(a dot b)
=(1 3 -2) dot (0 1 2)
=(1*0)+(3*1)+(-2*2)
=0+3-4
=-1
a dot a=(1^2)+(3^2)+(-2^2)
=1+9+4
=14
now [(a dot b)/a dot a]=-1/14
now {[(a dot b)/a dot a]}b=(-1/14)(0, 1, 2)
=(0,-1/14,-2/14)