The value of i ( j k) + j ( i k) + k ( i j) is 0 - 1 1 3

[Correct option is c] i ( j k) + j ( i k) + k ( i j) = i i + j ( - j) + k k = i i - j j + k k = 1 - 1 + 1 = 1

Vector Algebra — Class 12 Maths Solution

ncert misc SA NCERT,Page 459,Misc,Q.No 18

Question

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

• $0$

• $- 1$

• $1$

• $3$

Step-by-step Solution

[Correct option is c]

$\hat i \cdot (\hat j \times \hat k) + \widehat j \cdot (\hat i \times \hat k) + \hat k \cdot (\hat i \times \widehat j) = \hat i \cdot \hat i + \widehat j \cdot ( - \widehat j) + \hat k \cdot \hat k$

$= \hat i \cdot \hat i - \hat j \cdot \hat j + \hat k \cdot \hat k = 1 - 1 + 1 = 1$

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