Find the following (using magnitudes of vectors)

Question

a= (-3 6)

b= (4 1)

Find: a) |a+2b|

The answer is square root of 89

I know how to calculate the magnitude of a vector but I can't solve the sum or multiplication of their magnitudes. Please could someone help me.

(Sorry for representing badly the vetors a and b)

Answer 1

$\vec{a} + 2\vec{b} = (-3,6) + 2(4,1)$

= $(-3,6) + (8,2)$

= $(5,8)$

$\vec{a} + 2\vec{b} = \sqrt{5^2 + 8^2}$

=$\sqrt{25+64} = \sqrt{89}$

Answer 2

Hint:

$$\vec a+2\vec b=(-3,6)+(8,2)=(5,8)\;,\;\;\text{and}\;\;\left\|(5,8)\right\|=\sqrt{5^2+8^2}\;\ldots$$