pls show detailsthx 1 Consider the vectors v1 a Find the pro

pls show details.thx

1. Consider the vectors v1 (a Find the projection, proj1(v2), of v2 on v1 and draw a somewhat accurate picture to show the vectors and the projection. (b) Find the projection, proju2(v1), of vi on v2 and draw a somewhat accurate picture to show the vectors and the projection.

Solution

1)

Solution:

proj v2 v1 = (v1 · v2 )v2 / |v|2

|proj ba| = v1 · v2/|v2|

Calculate dot product:

v1 · v2 = v1x · v2x + v1y · v2y = 3 · 1 + 2 · 2 = 3 + 4 = 7
Calculate magnitude of a vector:

|v2| = v2x2 + v2y2 = 1^2 + 2^2 = 1 + 4 = 5

proj v2 v1 =    7/5 {   1   ;    2   } = {   7/ 5    ;    14 /5    }

|proj v2 v1| = 7/5        3.1304951684997055

a).

Calculate dot product:

v1.v2 = a_x · b_x + a_y · b_y = 1 · 3 + 2 · 2 = 3 + 4 = 7

Calculate magnitude of a vector:

|v1| = v1_x² + v1_y² = 3² + 2² = 9 + 4 = 13

proj b1v2 =	7	{	3	;	2	} = {	21/13	;	14/13	}
13