CameraIcon

SearchIcon

MyQuestionIcon

1

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

Intersection of Sets

If a1, b1, c1...

Question

If $^{1},^{1},^{1}$ is the reciprocal system of vector triad of $\to a, \to b, \to c$ , then $\to a \times^{1} + \to b \times^{1} + \to c \times^{1}$ is:

A

\to 0

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

B

\to a

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

C

\to b

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

D

\to c

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

Open in App

Solution

The correct option is A $\to 0$
We know, for the reciprocal system, $^{1} = \frac{\to b \times \to c}{[\to a \to b \to c]}$
Similarly, $^{1} = \frac{\to c \times \to a}{[\to a \to b \to c]}$
and $^{1} = \frac{\to a \times \to b}{[\to a \to b \to c]}$
Hence $\to a \times^{1} + \to b \times^{1} + \to c \times^{1} = Σ \to a \times \frac{(\to b \times \to c)}{[\to a \to b \to c]} = \frac{[(\to a \cdot \to c) \to b - (\to a \cdot \to b) \to c] + [(\to b \cdot \to a) \to c - (\to b \cdot \to c) \to a] + [(\to c \cdot \to b) \to a - (\to c \cdot \to a) \to b]}{[\to a \to b \to c]} = 0$

Suggest Corrections

thumbs-up

0

Similar questions

\to p, \to q, \to r

is reciprocal system of vector triad

\to a, \to b

\to c,

[\to a \to b \to c] [\to p \to q \to r] =

\to a =^i +^j +^k, \to b = 2^i +^k, \to c =^i + 2^j + 3^k

, then the ascending order the following is

A . [\to a \times \to b \to b \times \to c \to c \times \to a]

B . [\to a + \to b \to b + \to c \to c + \to a]

C . [\to a \to b \to c] [{\to a}^{1} {\to b}^{1} {\to c}^{1}]

D . [\to a - \to b \to b - \to c \to c - \to a]

^{1},^{1},^{1}

is the reciprocal system of vector triad of

\to a, \to b, \to c

\to a .^{1} + \to b .^{1} + \to c .^{1} =

^{1},^{1},^{1}

is the reciprocal system of vector triad of

\to a, \to b, \to c

(\to a + \to b) \cdot^{1} + (\to b + \to c) \cdot^{1} + (\to c + \to a) \cdot^{1} =

\to a, \to b, \to c

are three non-coplanar vectors, and

\to p, \to q, \to r

are reciprocal vectors to

\to a, \to b, \to c

respectively, then

(l \to a + m \to b + n \to c) . (l \to p + m \to q + n \to r)

: (

l, m, n

)

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Intersection of Sets

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon