Question

resultant of the product of two vectors always gives a vector, true or false? explain.

Answer 1

False, vectors are not products

Answer 2

HELLO THERE!

The answer to your question depends, whether the product is dot product or cross product.

Consider two vectors, A and B, where A = 3i and B = 3i + 4j.

When you calculate the dot product (scalar product),

A.B = 3i . (3i + 4j)

= 9 (which is a magnitude or value).

So in case of dot product, the resultant is not a vector.

Now, when you do the cross product of the two vectors,

A x B = 3i x (3i + 4j)

= -12k (which has a magnitude and direction, hence is a vector).

So, in case of cross product, the resultant is a vector.

Now, the straight-forward answer to your question is FALSE, because resultant of the product of two vectors does not always give a vector. In case of dot product, the resultant is not a vector.

HOPE MY ANSWER IS SATISFACTORY...

Please correct me if I am wrong :)