Find the Norm [[14/5],[2/5]]

Problem

‖[14/5],[2/5]‖

Solution

1. Identify the formula for the Euclidean norm (also known as the L2 norm) of a vector v=[[x],[y]] which is ∥v∥=√(,x2+y2)

2. Substitute the given components x=14/5 and y=2/5 into the norm formula.

‖[14/5],[2/5]‖=√(,(14/5)2+(2/5)2)

3. Square the individual components.

(14/5)2=196/25

(2/5)2=4/25

4. Sum the squared components inside the square root.

196/25+4/25=200/25

5. Simplify the fraction inside the square root.

200/25=8

6. Evaluate the square root to find the final magnitude.

√(,8)=2√(,2)

Final Answer

‖[14/5],[2/5]‖=2√(,2)

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