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Question

If a,band c are three vectors such that a×b=c and b×c=a, then


A

abc

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B

a=b=c

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C

abc1

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D

a,band c are orthogonal in pairs.

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Solution

The correct option is D

a,band c are orthogonal in pairs.


Explanation for the correct option:

Step1. Find the relation between a and b:

Given a=bxc

=bx(axb) ( given)

=(b.b)a(b.a)b

a=|b|2a(b.a)b

Comparing both the sides

|b|2=1;(b.a)=0|b|=1;(a.b)=0

Therefore, a is perpendicular to b

Step2. Find the relation between b and c:

Now, c=axb

=(bxc)xb=(b.b)c(b.c)b

c=|b|2c(b.c)b

On comparing both the sides

|b|2=1and(b.c)=0

Therefore, bis perpendicular to c.

Hence, the correct option is D.


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