Find u 2u 12v u v u v and u v u 4 7 v 3 3 u v 2u 12

Find |u|, |2u|, |1/2v|, |u + v|, |u - v|, and |u| - |v| u - (4, 7), v = (-3, -3) |u| = |v| = |2u| = |1/2 v| = |u + v| = |u - v| = |u| = |v| =

Solution

given u=3i+j , v=4i-5j

|u|=[(3)²+(1)²]=10

|v|=[(4)²+(-5)²]=41

2u=2(3i+j)=6i+2j

|2u|=[(6)²+(2)²]=40

(1_/2)v=(4_/2)i-(5_/2)j

|(1_/2)v|=[(4_/2)²+(-5_/2)²]=(41_/4)

u+v=(3i+j)+(4i-5j)=7i-4j

|u+v|=[(7)²+(-4)²]=65

u-v=(3i+j)-(4i-5j)=-1i+6j

|u-v|=[(-1)²+(6)²]=37

|u|-|v|=10 - 41