Question

Three non zero vectors Ā, B & C satisfy the relation Ā. B = 0& A.C=0. Then A can be parallel to
(A) B
(B) C
(C) B.C
(D) B×C
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Answer 1

Answer:

Firstly they are non zero vectors .

$\vec{A}.\vec{B}=0\\\\\implies ABcos\theta=0\\\\\implies cos\theta=0\\\\\implies \theta=90^\circ$

$\vec{A}.\vec{C}=0\\\\\implies AC cos\theta=0\\\\\implies cos\theta=0\\\\\implies \theta=90^\circ$

So the angle between A and C and A and B is 90° . A is perpendicular to both B and C .

Hence vector A will be parallel to B × C .

$\vec{B}\times \vec{C}$ will produce another vector perpendicular to both B and C whereas we already know that A is perpendicular to B and C . Hence Vector A is parallel to the cross product of B and C .

Hence OPTION D is correct .

Answer 2

Answer:

Explanation:

Vectors:-

It is given here that all three vectors are having a non-zero magnitude.

The vectors A,C and A,B are perpendicular to each other.

Two vectors are said to be parallel,if their cross product is 0.

So,A,B and C are automatically eliminated.

We are calculating triple vector product A,B,C that is, A*(B*C),where '*' denotes vector product.

Formula of A*(B*C)= (A.C)B-(A.B)C ,where '.' and '*' denote dot product and vector product respectively.

Applying the formula,we get 0.

Hence,A is parallel to (B*C)