The value of i ( j k )+ j ( i k )+ k ( i j ) is - Vidyadip

MCQ

$\text{The value of}\ \hat{\text{i}}\cdot(\hat{\text{j}}\times\hat{\text{k}})+\hat{\text{j}}\cdot(\hat{\text{i}}\times\hat{\text{k}})+\hat{\text{k}}\cdot(\hat{\text{i}}\times\hat{\text{j}})\ \text{is}$

A
0
B
-1
✓
1
D
3

✓

Answer

Correct option: C.

1

$\hat{\text{i}}\cdot\Big(\hat{\text{j}}\times\hat{\text{k}}\Big)+\hat{\text{j}}\cdot\Big(\hat{\text{i}}\times\hat{\text{k}}\Big)+\hat{\text{k}}\cdot\Big(\hat{\text{i}}\times\hat{\text{j}}\Big)$
$=\hat{\text{i}}\cdot\hat{\text{i}}+\hat{\text{j}}\cdot\Big(-\hat{\text{j}}\Big)+\hat{\text{k}}\cdot\hat{\text{k}}$
$=1-\hat{\text{j}}\cdot\hat{\text{j}}+1$
=1-1+1
=1
The correct answer is C.

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