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Can the components of a vector be greater than the vector itself?

Can the components of a vector be greater than the vector itself?

Grade:Upto college level

2 Answers

AJIT AskiitiansExpert-IITD
68 Points
11 years ago

Dear Aniket ,

Component of a vector in particular direction is determined by the dot product of the vector with the unit vector in that direction .

now , dot product with a unit vector means multiplying the magnitude of vector with cosine of the angle between vector and unit vector. but cos of anything is always lesser than or equal to  1 so magnitude of component has to be less than or equal to that of the vector.

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Aniket Patra
48 Points
11 years ago

What u told is right.But component of a vector can be greater than the vector itself.As for example a null vector can have its component +5 and -5 directed opposite to each other.

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