NIMCET 2015 Question Paper with solutions

Question : 16 of 120

Marks: +1, -0

Let

a↖{}

and

b↖{→}

be two vectors. Which of the following vectors are not perpendicular to each other ?

Solution:

(a)

(a×b)⋅a=[a,b,a]=0

(b)

(a+b)⋅(a×b)=[a\;a\;b]+[b\;a\;b]=0+0=0

(c)

(a+b)⋅(a-b)=|a|^{2}-|b|^{2}≠0

(d)

(a-b)⋅(a×b)=[a\;a\;b]-[b\;a\;b]=0-0=0

Hence, option (c) is correct

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