Diketahui vektor u=(1,-3,2) v=(1,1,0) dan w=(2,2,-4).Tentukanlah a=|u+v|, b=|u|+|v| , c=|u+v|-|u|-|v| ,d=|w-u|

vektor

u  = ( 1,  - 3, 2)

v = (1, 1, 0)

w = (2, 2 , -4)

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a) u + v = {(1+1) , (-3 +1), (2+0)} = ( 2 , – 2 , 2)

|u + v | = √(2² +(-2)²+(2)² = √(4 + 4 + 4) = √12 = 2√3

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b) |u| = √(1²+ (-3)² +(2)² = √(1 +9 + 4)= √14

|v| = √(1² + 1² +0²)= √2

|u |+|v| = √14 + √2

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c. |u+ v| – |u| – |v| = 2√3 – √14 – √2

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d.  w – u  = {(2-1) , (2 + 3) , (-4 -2)}= { 1, 5, – 6 }

| w – u | = √(1² + 5² +(-6)² = √(1 + 25 + 36) = √62