Question

Find the cross product of the given vectors.

A = 4 i - j + k and B = i - 2 j - 4 k .

Answer 1

Answer:

Explanation:

THE CROSS PRODUCT OF

A =4 i- j+ k AND B = i - 2 j - 4 k   IS GIVEN BY USING THE DETERMINANT METHOD

: SO THE ANSWER IS 2 i + 17 j - 7 k

Answer 2

Answer:

$\displaystyle \vec A \times \vec B=6\hat{i}+17\hat{j}-7\hat{k}$

Explanation:

Given :

$\displaystyle \text{ \vec A=4\hat{i}-\hat{j}+\hat{k} and }\\\\\displaystyle \vec B=\hat{i}-2\hat{j}-4\hat{k}$

Here angle is not given.

So we will use determinant method.

                                                             

           i                     j                          k

          4                   - 1                          1

           1                     -2                       - 4

                                                                 

$\displaystyle \vec A \times \vec B=\hat{i} (4-(-2))-\hat{j}(-16-1)+\hat{k}(-8-(-1))\\\\\\\displaystyle \vec A \times \vec B=\hat{i} (4+2))-\hat{j}(-17)+\hat{k}(-8+1))\\\\\\\displaystyle \vec A \times \vec B=\hat{i} (6))-\hat{j}(-17)+\hat{k}(-7))\\\\\\\displaystyle \vec A \times \vec B=6\hat{i}+17\hat{j}-7\hat{k}$

Thus we get answer.

Extra points :

In case of cross product

$\displaystyle \hat{i}\times\hat{i}=0\\\\\displaystyle \hat{j}\times\hat{j}=0\\\\\displaystyle \hat{k}\times\hat{k}=0\\\\\displaystyle \hat{i}\times\hat{j}=1\\\\\displaystyle \hat{j}\times\hat{k}=1\\\\\displaystyle \hat{k}\times\hat{i}=1$