Question

define the cross product of 2 vectors. also write the geometric interpretation of the cross product.

Answer 1

If two vectors are given by:

$\vec{a}=a_1\vec{i}+a_2\vec{j}+a_3\vec{k},\vec{b}=b_1\vec{i}+b_2\vec{j}+b_3\vec{k}$

Then the cross product of the two vectors is given by:

$\vec{a}\times\vec{b}=Det\begin{bmatrix}{\vec{i}} & {\vec{j}} & {\vec{k}} \\ {a_1} & {a_2} & {a_3} \\ {b_1} & {b_2} & {b_3}\end{bmatrix}$

Here Det means determinant of the matrix given.

The geometric interpretation of the cross product is given by the figure shown below:

From the above figure if a and b are two vectors then the cross product represents a vector that is mutually perpendicular to both a and b.