If r-a-0-r-b-0-r-c-0 where a-b-c- are non-coplanar- then

The correct option is A r⃗=0 The above equations imply, that either r⃗ is perpendicular to a⃗ , b⃗ and c⃗ or r⃗=0 However, ...

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

Byju's Answer

Standard XII

Mathematics

Solving System of Linear Equations Using Inverse

If r⃗.a⃗=0,...

Question

If $\to r . \to a = 0, \to r . \to b = 0, \to r . \to c = 0$ where $\to a, \to b, \to c$ are non-coplanar, then

\to r = 0

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

\to r

is perpendicular to

(\to a \times \to b)

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

\to r

is perpendicular to

(\to b \times \to c)

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

\to r

is perpendicular to

(\to c \times \to a)

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

Open in App

Solution

The correct option is A $\to r = 0$
The above equations imply, that either $\to r$ is perpendicular to $\to a$ , $\to b$ and $\to c$ or $\to r = 0$
However, $\to a$ , $\to b$ , $\to c$ are no-coplanar, therefore, $\to r = 0$

Suggest Corrections

Similar questions

Q. If

\to a, \to b, \to c

are three non-coplanar non-zero vectors and

\to r

is any vector, then

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b) =

Q. If

\to a, \to b, \to c

be three non-coplanar vectors and

\to r

be any arbitrary vector, then

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c) \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)

is equal to?

Q. Assertion :A vector

\to R

can be expressed as a linear combination of a vector

\to A

and another vector perpendicular to

\to A

and coplanar with

\to R

and

\to A

as,

\to R = (\frac{\to R . \to A}{\to A . \to A}) \to A - (\frac{1}{\to A . \to A}) (\to A \times (\to A \times \to R))

Reason: If

\to a, \to b, \to c

are coplanar then

\to a + \to b, \to b + \to c, \to c + \to a

are also coplanar.

Q. If

\to a, \to b, \to c

are three noncoplanar nonzero vectors and

\to r

is any vector in space then

(\to a \times \to b) \times (\to r \times \to c) + (\to b \times \to c \times (\to r \times \to a) + (\to c \times \to a) \times (\to r \times \to b)

is equal to

Q. If

\to r \times \to b = \to c \times \to b & \to r, \to a = 0

where

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

then

\to r

Join BYJU'S Learning Program

If →r.→a=0,→r.→b=0,→r.→c=0 where →a,→b,→c are non-coplanar, then

The correct option is A →r=0The above equations imply, that either →r is perpendicular to →a ,→b and →c or →r=0However, →a ,→b,→c are no-coplanar, therefore, →r=0

If $\to r . \to a = 0, \to r . \to b = 0, \to r . \to c = 0$ where $\to a, \to b, \to c$ are non-coplanar, then

The correct option is A $\to r = 0$
The above equations imply, that either $\to r$ is perpendicular to $\to a$ , $\to b$ and $\to c$ or $\to r = 0$
However, $\to a$ , $\to b$ , $\to c$ are no-coplanar, therefore, $\to r = 0$