If `a=2i+5j-7k ,\ b=-3i+4j+k\ a n d\ c=i-2j-3k ,\ ` compute `( vec axx vec b)xx vec c` and `axx(bxxc)` and verify that these are not equal.

Explanation

Given that

`a=2i+5j-7k ,\ b=-3i+4j+k\ a n d\ c=i-2j-3k`
`therefore vec{a} times vec{b}=|hat{i}\ hat{j}\ hat{k} \ 2 \ 5\ -7 \-3\ 4\ 1|`

`=(5+28) hat{i}-(2-21) hat{j}+(8+15) hat{k}`

`=33 hat{i}+19 hat{j}+23 hat{k}`

`Rightarrow(vec{a} times vec{b}) times vec{c}=|hat{i} \hat{j} \ hat{k} \ 33\ 19\ 23 \ 1 \-2 \ -3|`

`=(-57+46) hat{i}-(-99-23) hat{j}+(-66-19) hat{k}`

`Rightarrow(vec{a} times vec{b}) times vec{c}=-11 hat{i}+122 hat{j}-85 hat{k} ldots(1)`

`therefore vec{b} times vec{c}=|
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