(1) a+2b=(3,−1)+2(2,4)=(7,7)a + 2b = (3,-1) + 2(2,4) = (7,7)a+2b=(3,−1)+2(2,4)=(7,7) (2) a+32b+2c=(3,−1)+32(2,4)+2(−2,1)=(2,7)a + \frac{3}{2}b + 2c = (3,-1) + \frac{3}{2}(2,4) + 2(-2,1) = (2,7)a+23b+2c=(3,−1)+23(2,4)+2(−2,1)=(2,7) (3) ∣a∣=32+(−1)2=10|a| = \sqrt{3^2+(-1)^2} = \sqrt{10}∣a∣=32+(−1)2=10 (4) ∣b+2c∣=∣(2,4)+2(−2,1)∣=∣(−2,6)∣=(−2)2+62=40=210|b+2c| = |(2,4)+2(-2,1)| = |(-2,6)| = \sqrt{(-2)^2+6^2} = \sqrt{40} = 2\sqrt{10}∣b+2c∣=∣(2,4)+2(−2,1)∣=∣(−2,6)∣=(−2)2+62=40=210 (5) a⋅b=3⋅2+(−1)⋅4=2a\cdot b = 3\cdot 2 + (-1)\cdot 4 = 2a⋅b=3⋅2+(−1)⋅4=2 (6) (a+b)⋅c={(3,−1)+(2,4)}⋅(−2,1)=(5,3)⋅(−2,1)=5⋅(−2)+3⋅1=−10+3=−7(a+b)\cdot c = \{(3,-1)+(2,4)\}\cdot(-2,1) = (5,3)\cdot(-2,1) = 5\cdot(-2)+3\cdot 1 = -10+3 = -7(a+b)⋅c={(3,−1)+(2,4)}⋅(−2,1)=(5,3)⋅(−2,1)=5⋅(−2)+3⋅1=−10+3=−7