The value of is (A) 0 (B) –1 (C) 1 (D) 3

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Solution

The given expression is i ^ ⋅( j ^ × k ^ )+ j ^ ⋅( i ^ × k ^ )+ k ^ ⋅( i ^ × j ^ )

Calculate the value of the given expression.

i ^ ⋅( j ^ × k ^ )+ j ^ ⋅( i ^ × k ^ )+ k ^ ⋅( i ^ × j ^ )= i ^ ⋅ i ^ + j ^ ⋅( − j ^ )+ k ^ ⋅( k ^ ) = i ^ ⋅ i ^ − j ^ ⋅ j ^ + k ^ ⋅ k ^ (1)

The formula for dot product of i ^ , j ^ , k ^ is,

i ^ ⋅ i ^ =| i ^ || i ^ |cos0 =1×1×1 =1

Similarly,

j ^ ⋅ j ^ =| j ^ || j ^ |cos0 =1×1×1 =1

And,

k ^ ⋅ k ^ =| k ^ || k ^ |cos0 =1×1×1 =1

Substitute these values in equation (1).

i ^ ⋅ i ^ − j ^ ⋅ j ^ + k ^ ⋅ k ^ =1−1+1 i ^ ⋅ i ^ − j ^ ⋅ j ^ + k ^ ⋅ k ^ =1

Thus, the correct option is (C).

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