A- b- c- are three non coplanar non zero vectors and r- is any vector in space- then a-b- - r-c- - b-c- - r-a- - c-a- - r-b- is equal to

The correct option is B 2[ a⃗ b⃗ c⃗ ]r⃗ The value of ( a⃗×b⃗ #160; ) ×( r⃗×c⃗ #160; ) +( b⃗×c⃗ #160; ) ×( r⃗×a⃗ #160; ) +( c⃗×a⃗ #160; ) ×( ...

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

Consistency of Linear System of Equations

a⃗, b⃗, c⃗ ar...

Question

$\to a, \to b, \to c$ are three non coplanar non zero 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

2 [\begin{matrix} \to a & \to b & \to c \end{matrix}] \to r

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

3 [\begin{matrix} \to a & \to b & \to c \end{matrix}] \to r

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

[\begin{matrix} \to a & \to b & \to c \end{matrix}] \to r

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

Suggest Corrections

Similar questions

\to a, \to b, \to c

\to r

[\to b \to c \to r] \to a + [\to c \to a \to r] \to b + [\to a \to b \to r] \to c

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

¯ ¯ ¯ p, ¯ ¯ ¯ q, ¯ ¯ ¯ r

\to p = \frac{\to b \times \to c}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}, \to q = \frac{\to c \times \to a}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}, \to r = \frac{\to a \times \to b}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}

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

\to a, \to b, \to c

\to p = \frac{\to b \times \to c}{[\to a \to b \to c]}

\to q = \frac{\to c \times \to a}{[\to a \to b \to c]}

\to r = \frac{\to a \times \to b}{[\to a \to b \to c]}

(2 \to a + 3 \to b + 4 \to c) . \to p + (2 \to b + 3 \to c + 4 \to a) . \to q +

(2 \to c + 3 \to a + 4 \to b) . \to r =

\to a, \to b, \to c

\to r

(\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) =

\to a, \to b, \to c

\to p, \to q, \to r

\to p = \frac{\to b \times \to c}{[\begin{matrix} \to b & \to c & \to a \end{matrix}]}

\to q = \frac{\to c \times \to a}{[\begin{matrix} \to c & \to a & \to b \end{matrix}]}

\to r = \frac{\to a \times \to b}{[\begin{matrix} \to a & \to b & \to c \end{matrix}]}

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

Join BYJU'S Learning Program