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Q.

If a1 and a2 are two non-collinear unit vectors and if a1+a2=3, then the value of a1-a2·2a1+a2 is

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a

2

b

32

c

12

d

1

answer is C.

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Detailed Solution

Since, a1 and a2 are non-collinear.a1=a2=1a1+a2=3a12+a22+2a1a2cosθ=(3)21+1+2cosθ=3cosθ=12Now, a1-a2·2a1+a2=2a12-a22-a1a2cosθ =2-1-12=12
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If a1 and a2 are two non-collinear unit vectors and if a1+a2=3, then the value of a1-a2·2a1+a2 is