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Question
The value of `hati(hatj + hatk)hatj * (hati + hatk) + hatk - (hati + hatj)` is-
Options
0
–1
1
3
MCQ
Solution
1
Explanation:
`|hati, hatj, hatk|` are the perpendicular unit vectors, we know,
∴ `hati xx hatj = hatk, hatj, hatk = hati, hatk xx hati = hatj`
And `hati * hatj` = 1, `hatj * hatj` = 1 and `hatk * hatk` = 1
⇒ `hati * (hatj xx hatk) + hatj * (hati xx hatk) + hatk * (hati * hatj)`
= `hati * (hatj xx hatk) - hatj * (hatk xx hati) + hatk * (hati xx hatj)` .......`[because hati xx hatk = - hatk xx hati]`
= `hati * hati - hatj * hatj + hatk * hatk`
= 1 + 1 + 1
= 1
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