Vectors> is component of a vector is lso a vector?...

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

ivmsudhana sarma , 7 Years ago

Grade 12

1 Answers

Aksh

Last Activity: 7 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.