Question

Assertion: Statement I: The dot product of one vector with another vector may be a scalar or a vector.

Reason: Statement-II: The product of two vectors is a vector quantity, then the product is called a dot product.

• A. Statement-I is false, Statement-II is true.
• B. Both Statement-I and Statement-II are false.
• C. Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
• D. Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for Statement-I.

Answer 1

1. Dot product of two vectors $\overrightarrow{a}and\overrightarrow{b}$ is given by$\overrightarrow{a}.\overrightarrow{b}=\left|\overrightarrow{a}\right|\left|\overrightarrow{b}\right|\cos \theta$ .
2. The dot product of two vectors is always gives a scalar.

3. That is why it is also called scalar product.

4. The cross-product of two vectors is always a vector. Thus, both statements are incorrect.

The correct option is B - Both Statement-I and Statement-II are false.​