can the vector components be negative

kariboucnp

kariboucnp

Answered

2022-12-31

can the vector components be negative

Answer & Explanation

abbrechtq17

abbrechtq17

Expert

2023-01-01Added 5 answers

Step 1
Yes, a vector component may be negative. It depends on along which direction we wish to calculate that component.
If a vector A = 2 i + 3 j, find its components along i + j and i j
Component of A along B is A B ^ where B ^ = B | B | is a unit vector along B
Step 2
Component Along i ^ + j ^ is A ( i ^ + j ^ ) 1 2 + 1 2 = ( 2 i ^ + 3 j ^ ) ( i ^ + j ^ ) 2
= 2 + 3 2 = 5 2
Component along i ^ j ^ is A ( i ^ j ^ ) 2 = ( 2 i ^ + 3 j ^ ) ( i ^ j ^ ) 2
= 2 3 2 = 1 2

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