how to find length of a vector
Vector length. Vector magnitude
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- Vector length - definition
- Vector length formulas
- for plane problems
- for spatial problems
- for n dimensional space problems
- Examples of tasks
- plane tasks
- spatial tasks
- n dimensional space tasks
Vector length - definition
Definition.
The length of the directed segment determines the numerical value of the vector is called the length of vector AB.
The magnitude of a vector is the length of the vector.
The length of the vector AB is denoted as |AB|.
Basic relation. The length of vector |a| in Cartesian coordinates is the square root of the sum of the squares of its coordinates.
Vector length formulas
Vector length formula for two-dimensional vector
In the case of the plane problem the length of the vector a = {ax ; ay } can be found using the following formula:
Vector length formula for three-dimensional vector
In the case of the spatial problem the length of the vector a = {ax ; ay ; az } can be found using the following formula:
Vector length formula for arbitrary dimensions vector
In the case of the n dimensional space problem the length of the vector a = {a 1 ; a 2; ... ; an } can be found using the following formula:
Examples of tasks
Examples of plane tasks
Example 1. Find the length of the vector a = {2; 4}.
Solution: |a| = √22 + 42 = √4 + 16 = √20 = 2√5.
Example 2. Find the length of the vector a = {3; -4}.
Solution: |a| = √32 + (-4)2 = √9 + 16 = √25 = 5.
Examples of spatial tasks
Example 3. Find the length of the vector a = {2; 4; 4}.
Solution: |a| = √22 + 42 + 42 = √4 + 16 + 16 = √36 = 6.
Example 4. Find the length of the vector a = {-1; 0; -3}.
Solution: |a| = √(-1)2 + 02 + (-3)2 = √1 + 0 + 9 = √10.
Examples of n dimensional space tasks
Example 5. Find the length of the vector a = {1; -3; 3; -1}.
Solution: |a| = √12 + (-3)2 + 32 + (-1)2 = √1 + 9 + 9 + 1 = √20 = 2√5
Example 6. Find the length of the vector a = {2; 4; 4; 6 ; 2}.
Solution: |a| = √22 + 42 + 42 + 62 + 22 = √4 + 16 + 16 + 36 + 4 = √76 = 2√19.
how to find length of a vector
Source: https://onlinemschool.com/math/library/vector/length/
Posted by: williamscrou1946.blogspot.com
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