Question

Assertion: The cross product of a vector with itself is a null vector.
Reason: The cross-product of two vectors results in a vector quantity.
(A) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(B) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(C) If the assertion is true but the reason is false.
(D) If the assertion and reason both are false.

Answer 1

Hint:
In three dimensions, the cross product is a basic operation on two vectors. A vector that is perpendicular to both vectors is produced as an outcome.$\vec{A}\times \vec{B}$Stands for the vector product of two vectors,$\vec{A}$ and $\vec{B}$ . The resulting vector is perpendicular to both $\vec{A}$ and$\vec{B}$.

Formula used:
\[\vec A \times \vec B = \left| A \right|\left| B \right|\sin \theta \]


Complete step by step solution:
Cross product is a type of vector multiplication that is carried out between two vectors of various forms or natures. There is a magnitude as well as a direction to a vector. The dot product and cross product can be used to multiply two or more vectors. The resultant vector is known as the cross product of two vectors or the vector product when two vectors are multiplied together and the product of the vectors is likewise a vector variable.
Formula for Cross product of two vectors
Let’s us assume two vectors $\vec A$and $\vec B$
Then the cross product of these vectors can be written as,
$\vec A \times \vec B = \left| A \right|\left| B \right|\sin \theta $
In these given questions, assertion is correct because the cross product of the vector with itself is a null vector because angle between both the vectors will be zero and reason is also correct because cross product of two vectors results in vector quantity but it is not a correct explanation of given assertion.
Therefore, if both assertion and reason are true but reason is not the correct explanation of the assertion




Therefore, the correct option is B.




Note:
We need to have a clear grasp of the concept of the cross product of vectors to solve such questions. The cross-product features are useful for understanding vector multiplication clearly and for quickly resolving any issues that may arise when performing vector calculations.