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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

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

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B \times C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B \cdot C

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

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

Suggest Corrections

Similar questions

Q. Three vectors

A

B

and

C

satisfy the relation

A \cdot B = 0

and

A \cdot C = 0

. Then the vector

A

is parallel or anti-parallel to

Q. If the three vectors

A, B

and

C

satisfy the relation

A \cdot B = 0

and

A \cdot C = 0

, then vector

A

is parallel to

Q. Three vectors

A

B

and

C

satisfy the relation

A \cdot B = 0

and

A \cdot C = 0

. Then the vector

A

is parallel or anti-parallel to

Q. Three non-zero vectors

\to A, \to B

\to C

satisfy the relation

\to A . \to B = 0

\to A . \to C = 0

. Then

\to A

can be parallel to

Q. Let

a, b

and

c

be a system of three non-coplanar vectors. Then the system

a^{'}, b^{'}

and

c^{'}

which satisfies

a \cdot a^{'} = b \cdot b^{'} = c \cdot c^{'} = 1

and

a \cdot b^{'} . = a \cdot c^{'} = b \cdot a^{'} . = b \cdot c^{'} = c \cdot a^{'} = c \cdot b^{'} = 0

is called the reciprocal system to the vectors

a, b

and

c

a \times a^{'} + b \times b^{'} + c \times c^{'}

is a

Join BYJU'S Learning Program

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: