Find the Norm [[8],[-16],[11]]

Problem

‖[8],[−16],[11]‖

Solution

1. Identify the components of the vector v=[[8],[−16],[11]] as (v_1)=8 (v_2)=−16 and (v_3)=11

2. Apply the formula for the Euclidean norm (magnitude) of a vector in ℝ3 which is ∥v∥=√(,(v_1)2+(v_2)2+(v_3)2)

3. Square each component of the vector.

8=64

(−16)2=256

11=121

4. Sum the squared components together.

64+256+121=441

5. Take the square root of the sum to find the final norm.

√(,441)=21

Final Answer

‖[8],[−16],[11]‖=21

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