Question

Two vectors a and b are $a=3i,b=j+3k$. Find $a\times b$

Answer 1

The cross product of two vectors is defined as a vector that is perpendicular to both the initial vectors, with a direction that is chosen as right hand rule and magnitude equal to area of parallelogram that vectors form into.
Formula used:
$a\times b=ab\sin \theta$

Complete answer:
Let us write down the given two vectors,$\begin{aligned} & a=3i+0j+0k \\\ & b=0i+1j+3k \\\ \end{aligned}$
The cross product between these two products is given as,$\begin{aligned} & a\times b=(3i+0j+0k)\times (0i+1j+3k) \\\ & a\times b=(3\times 0)(i\times i)+(0\times 1)(j\times j)+(0\times 3)(k\times k)+(3\times 1)(i\times j)+(3\times 3)(i\times k)+0 \\\ & a\times b=3k+9j \\\ \end{aligned}$
Therefore, the cross product between two vectors is found as above.

Additional Information:
In mathematics the cross product or vector product is a binary operation on 2 vectors in 3-dimensional space. Given to linearly independent vectors, the cross product is a vector perpendicular to go to A&B.; The result and vector are normal to the plane containing da to initial vectors. It has many applications in mathematics, engineering and computer programming. It should not be confused with the dot product. If 2 vectors have the same direction and have the exact opposite direction from one another, the cross product is equal to zero. The magnitude of the product is the area of parallelogram with the vectors for sides, magnitude of the product of the 2 perpendicular vectors is the product of their lengths. Like the dot product, it depends on the metric of the Euclidean space button like the dot product, it also depends on the choice of orientation.

Note:
The cross product of two vectors is the product of the magnitudes of the two vectors and the sine of the angle between them. Whereas, the dot product is the product of the magnitudes of the two vectors and the cosine of the angle between them.