If A-B-C are non coplanar vectors then A-B-CC-A-B-B-A-CC-A-B-

A.B×CC×A.B+B.A×CC.A×B = [ABC][CAB] + nbsp; [BAC][CAB] nbsp; = [ABC][ABC] nbsp; + nbsp; [BAC][ABC] nbsp; = [ABC] [ABC] nbsp; [ABC] ...

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

Condition for Coplanarity of Four Points

If A,B,C ar...

Question

If $\to A, \to B, \to C$ are non coplanar vectors then $\frac{\to A . \to B \times \to C}{\to C \times \to A . \to B} + \frac{\to B . \to A \times \to C}{\to C . \to A \times \to B} =$

Open in App

Solution

Suggest Corrections

Similar questions

\to a, \to b, \to c

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

a, b, c

∣ ∣ ∣ ∣ \begin{matrix} a & b & c a . a & a . b & a . c b . a & b . b & b . c \end{matrix} ∣ ∣ ∣ ∣ =

[¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] = 1

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

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

¯ ¯ ¯ a + ¯ ¯ b + ¯ ¯ c = ¯ ¯ ¯ 0

¯ ¯ ¯ a . ¯ ¯ b + ¯ ¯ b . ¯ ¯ c + ¯ ¯ c . ¯ ¯ ¯ a =

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

| ¯ ¯ ¯ a | = 1, | ¯ ¯ b | = 2, | ¯ ¯ c | = 3

¯ ¯ ¯ a . ¯ ¯ b = ¯ ¯ b . ¯ ¯ c = ¯ ¯ c . ¯ ¯ ¯ a = 0

| [¯ ¯ ¯ a ¯ ¯ b ¯ ¯ c] | =

Join BYJU'S Learning Program