If a- b-a- c and a- b-a- c- then

The correct option is A either a=0 or b=c Given, nbsp; a· b=a· c and a× b=a× c, ⇒ a· (b c) = 0 and a× (b c) = 0 Hence nbs ...

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

Byju's Answer

Standard XII

Chemistry

Octet Rule

If a· b=a· ...

Question

If $a \cdot b = a \cdot c$ and $a \times b = a \times c,$ then

either

a = 0

b = c

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

a

is parallel to

(b - c)

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

a

is perpendicular to

(b - c)

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

None of these

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

Open in App

Solution

The correct option is A either $a = 0$ or $b = c$
Given, $a \cdot b = a \cdot c$ and $a \times b = a \times c,$
$\Rightarrow a \cdot (b - c) = 0$ and $a \times (b - c) = 0$
Hence either $a = 0$ or $b = c$

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. 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 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

\to a =^i +^j +^k

and

\to b =^j -^k .

\to c

is a vector such that

\to a \times \to c = \to b

and

\to a \cdot \to c = 3,

then

\to a \cdot (\to b \times \to c)

is equal to

Join BYJU'S Learning Program

If a⋅b=a⋅c and a×b=a×c, then

The correct option is A either a=0 or b=cGiven, a⋅b=a⋅c and a×b=a×c, ⇒a⋅(b−c)=0 and a×(b−c)=0Hence either a=0 or b=c

If $a \cdot b = a \cdot c$ and $a \times b = a \times c,$ then

The correct option is A either $a = 0$ or $b = c$
Given, $a \cdot b = a \cdot c$ and $a \times b = a \times c,$
$\Rightarrow a \cdot (b - c) = 0$ and $a \times (b - c) = 0$
Hence either $a = 0$ or $b = c$