Three vectors satisfy the relation A- B - 0 and A- C - 0- then A is parallel to-

The correct option is B B× C ∵ A . B =0 and A . C =0 ∴ A is perpendicular to both A and C,hence A must be p ...

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Byju's Answer

Standard XII

Chemistry

Arrhenius Equation

Three vectors...

Question

Three vectors satisfy the relation $A \cdot B = 0$ and $A \cdot C = 0,$ then $A$ is parallel to:

C

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B

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B \times C

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B \cdot C

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Solution

The correct option is B $B \times C$
$∵ ¯ ¯¯ ¯ A . ¯ ¯¯ ¯ B = 0$
$a n d ¯ ¯¯ ¯ A . ¯ ¯¯ ¯ C = 0$
$∴ ¯ ¯¯ ¯ A i s p e r p e n d i c u l a r t o b o t h A a n d C, h e n c e$
$A m u s t b e p a r a l l e l t o a v e c t o r t h a t i s p e r p e n d i c u l a r$
$t o b o t h ¯ ¯¯ ¯ B a n d ¯ ¯¯ ¯ C .$
$W e k n o w c r o s s p r o d u c t o f t w o v e c t o r s g i v e s a v e c t o r$
$p e r p e n d i c u l a r t o b o t h v e c t o r s .$
$H e n c e ¯ ¯¯ ¯ A m u s t b e p a r a l l e l t o (¯ ¯¯ ¯ B \times ¯ ¯¯ ¯ C) o r (¯ ¯¯ ¯ C \times ¯ ¯¯ ¯ B)$
$∴ C) A n s .$

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Three vectors satisfy the relation A⋅B=0 and A⋅C=0, then A is parallel to:

Three vectors satisfy the relation $A \cdot B = 0$ and $A \cdot C = 0,$ then $A$ is parallel to: