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Question

If b and c are any two non-collinear unit vectors and a is any vector, then
(a.b)b+(a.c)c+a.(b×c)|b×c|2(b×c)=

A
a
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B
b
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C
c
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D
a+b+c
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Solution

The correct option is A a
Given that b,c are unit vector

Let

b=^i

c=^j

a=^i+^k

=(ab)b+(ac)c+a(b×c)b×c2(b×c)

=(^i+^k)(^i)b+(^i+^k)(^j)c+(^i+^k)(^i×^j)^i×^j2(^i×^j)

=(1)^i+(0)c+(^i+^k)(^k)^k2(^k)

=^i+11(^k)

=^i+^k

=a

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