JEE Main2005MathematicsVector AlgebraActual

For any vectora a the value of ( a i )^2+( a j )^2+( a k )^2 is equal to

Options

A3 a ^2
Ba ^2
C2 a ^2
D4 a ^2

Correct answer

C. 2 a ^2

Step-by-step solution

Let a =x i +y j +z k aligned & a i =z j -y k & ( a i )^2=y^2+z^2 aligned similarly ( a j )^2=x^2+z^2 and ( a k )^2=x^2+y^2 ( a i )^2=y^2+z^2 similarly ( a j )^2=x^2+z^2 and ( a k )^2=x^2+y^2 ( a i )^2+( a j )^2+( a k )^2=2 (x^2+y^2+z^2 )=2 a ^2 .

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