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If a and b are unit vectors , (a+b)x(axb) is parallel to ________ . Ans – (a-b)

If a and b are unit vectors , (a+b)x(axb) is parallel to ________ .
 
Ans – (a-b)

Grade:12

1 Answers

Rajesh Sardar
32 Points
9 years ago
Let [(a+b)×(a×b)] = d.
Now cross product of (a-b) with d will be-
                               (a-b) × d= (a-b)×[(a+b)×(a×b)]
                                       =(a+b)[(a-b).(a×b)] – (a×b)[(a-b).(a+b)]
                                      = 0 –  (a×b)(a2-b2)           [ Since a.(a×b) and b.(a×b) both equals to 0
                                                                                 a×(b×c)= b(a.c) –  c(a.b)  ]
                                      = 0                                 [Since a and b are unit vector. Hence a2 - b2 =1-1=0]
So we have (a – b) × d = 0 and hence d is parallel to (a – b).
Therofore (a+b)×(a×b) is parallel to (a – b).

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