If A- B- C are three non-coplanar vectors- then find the value of A- B- C-C- A- B-B- A- C-C- A- B

The correct option is A 0 A.B× C=[ ABC ] ,C× A.B=[ ABC ] and A.B× C=[ ABC ] So nbsp; A.( B× C ) nbsp;/( C× A ) .B + B.( A× C ) nbsp;/ C.( ...

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

Byju's Answer

Standard XII

Physics

Introduction

If A, B, C ...

Question

If $A, B, C$ are three non-coplanar vectors, then find the value of $\frac{A \cdot (B \times C)}{(C \times A) \cdot B} + \frac{B \cdot (A \times C)}{C \cdot (A \times B)}$

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

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

Not defined

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

None of the above

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

Open in App

Solution

The correct option is A 0
$A . B \times C = [A B C], C \times A . B = [A B C]$ and $A . B \times C = [A B C]$
So $\frac{A . (B \times C)}{(C \times A) . B} + \frac{B . (A \times C)}{C . (A \times B)} = \frac{[A B C]}{[A B C]} - \frac{[A B C]}{[A B C]} = 0$

Suggest Corrections

Similar questions

Q. If

\to a, \to b, \to c

are non - coplanar vectors, then

\frac{a . (b \times c)}{(c \times a) . b} + \frac{b . (a \times c)}{c . (a \times b)} = ?

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^{'}, b^{'}, c^{'}

is a reciprocal system of

a, b, c

then

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

Find the correct one:

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

Q. If

a, b, c

are three non-coplanar vectors, then

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

is equal to

Join BYJU'S Learning Program

If A, B, C are three non-coplanar vectors, then find the value of A⋅(B×C)(C×A)⋅B+B⋅(A×C)C⋅(A×B)

The correct option is A 0A.B×C=[ABC],C×A.B=[ABC] and A.B×C=[ABC]So A.(B×C)(C×A).B+B.(A×C)C.(A×B)=[ABC][ABC]−[ABC][ABC]=0

If $A, B, C$ are three non-coplanar vectors, then find the value of $\frac{A \cdot (B \times C)}{(C \times A) \cdot B} + \frac{B \cdot (A \times C)}{C \cdot (A \times B)}$

The correct option is A 0
$A . B \times C = [A B C], C \times A . B = [A B C]$ and $A . B \times C = [A B C]$
So $\frac{A . (B \times C)}{(C \times A) . B} + \frac{B . (A \times C)}{C . (A \times B)} = \frac{[A B C]}{[A B C]} - \frac{[A B C]}{[A B C]} = 0$