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is component of a vector is lso a vector???please explain

is component of a vector is lso a vector???please explain
 

Grade:12

1 Answers

Aksh
31 Points
5 years ago
There are two cases for components of vectors to be vectors or scalarsCASE I Cross product(vector product)→Component (vector)Illustration:Let the angle between the vectors (a&b) = ka vector × b vector =|a||b|sink Therefore, the component of b vector on avector(b sink)=(a vector ×b vector)/|a|Since the numerator (cross product) is vector & denominator(|a|) is scalar, the component is a vector quantity.Case II Dot product(scalar product)→Component(scalar)Illustration:Let the angle between the vectors (a&b) = ka vector • b vector =|a||b|cos k Therefore, the component of b vector on avector(b cos k)=(a vector • b vector)/|a|Since the numerator (dot product) is scalar & denominator(|a|) is vector, the component is a scalar quantity.*Simply:-If we are dealing with:A) cross product, the component is vector.B) dot product, the component is scalar.

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