Question

Find the cross product of A=2i+3j+k and B =I -j +2k

Answer 1

Answer:

7i-3j-5k..............

Answer 2

Answer:

The cross product of the vectors A=2i+3j+k and B =I -j +2k is $7\hat{i}-3\hat{j}-5\hat{k}$.

Explanation:

This is the formula-based question.

The cross product of two vectors A and B is given as,

$\vec{A}\times \vec{B}=\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\a_1&a_2&a_3\\b_1&b_2&b_3\\\end{array}\right] =(a_2b_3-a_3b_2)\hat{i}-(a_1b_3-a_3b_1)\hat{j}+(a_1b_2-a_2b_1)\hat{k}$    (1)

And from the question we have,

$\vec{A}=2\hat{i}+3\hat{j}+\hat{k}$          (2)

$\vec{B}=\hat{i}-\hat{j}+2\hat{k}$             (3)

By using equations (2) and (3) in equation (1) we get;

$\vec{A}\times \vec{B}=\left[\begin{array}{ccc}\hat{i}&\hat{j}&\hat{k}\\2&3&1\\1&-1&2\\\end{array}\right] =(3\times2-1\times-1)\hat{i}-(2\times 2-1\times 1)\hat{j}+(2\times -1 -3\times 1)\hat{k}$

$\vec{A}\times \vec{B}=(6+1)\hat{i}-(4-1)\hat{j}+(-2-3)\hat{k}=7\hat{i}-3\hat{j}-5\hat{k}$

Hence, the cross product of the vectors A=2i+3j+k and B =I -j +2k is $7\hat{i}-3\hat{j}-5\hat{k}$.