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FIND THE VALUE OF i x ( i x a) + j x( j x a) + k x( k x a).where i,j,k are unit vectors along x,y and z axes and a is any vector

FIND THE VALUE OF i x ( i x a) + j x( j x a) +
k x( k x a).where i,j,k are unit vectors along x,y and z axes and a is any vector

Grade:Select Grade

3 Answers

Y RAJYALAKSHMI
45 Points
9 years ago
i x (i x a) = (i.a) i – (i.i)a = (i.a)i – a
j x (j x a) = (j.a) j – (j.j)a = (j.a)j – a
k x (k x a) = (k.a) k – (k.k)a = (k.a)k – a
i x ( i x a) + j x( j x a) + k x( k x a) = (i.a)i – a + (j.a)j – a + (k.a)k – a
= (i.a)i + (j.a)j + (k.a)k – 3a 
= a – 3a = –2a
 
Ans: –2a
 
Bharat Makkar
34 Points
9 years ago
thanks!!!!
 
ankit singh
askIITians Faculty 614 Points
3 years ago
x (i x a) = (i.a) i – (i.i)a = (i.a)i – a
j x (j x a) = (j.a) j – (j.j)a = (j.a)j – a
k x (k x a) = (k.a) k – (k.k)a = (k.a)k – a
i x ( i x a) + j x( j x a) + k x( k x a) = (i.a)i – a + (j.a)j – a + (k.a)k – a
= (i.a)i + (j.a)j + (k.a)k – 3a 
= a – 3a = –2a

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