If i , j , k are unit vectors, then - Vidyadip

MCQ

If $\hat{\text{i}},\hat{\text{j}},\hat{\text{k}}$ are unit vectors, then

A
$\hat{\text{i}}.\hat{\text{j}}=1$
✓
$\hat{\text{i}}.\hat{\text{i}}=1$
C
$\hat{\text{i}}\times\hat{\text{j}}=1$
D
$\hat{\text{i}}\times\big(\hat{\text{j}}\times\hat{\text{k}}\big)=1$

✓

Answer

Correct option: B.

$\hat{\text{i}}.\hat{\text{i}}=1$

Let us check each option one by one.

We know

$\hat{\text{i}}.\hat{\text{j}}=0$

$\neq1$

We know

$\hat{\text{i}}.\hat{\text{i}}=|\hat{\text{i}}|^2$

$=1^2$

$=1$

$\hat{\text{i}}\times\hat{\text{j}}=\hat{\text{k}}$

$\neq1$

$\hat{\text{i}}\times\big(\hat{\text{i}}\times\hat{\text{k}}\big)=\hat{\text{i}}\times\hat{\text{i}}$

$=0$

$\neq1$

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