Let r- be the only point of intersection of the planes r-a-P1- r-b-P2- r-c-P3 thenA- -a-b-c-0B- r-P1b-c-P2c-a-P3a-b-C- a- b- c- are non - coplanarD- r-a-b-c-P1b-c-P2c-a-P3a-b-

The correct options are C are non – coplanar D Let r⃗ = λ_1 (b⃗×c⃗) + λ_2 (c⃗×a⃗) + λ_3 (a⃗×b⃗) r⃗. a⃗ = λ_1 [ a⃗b⃗c⃗ ]⇒ P_1 = λ_1 [ a⃗b⃗c⃗ ] λ_1 = P_1/ [ a ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

Let r⃗ be the...

Question

Let $\to r$ be the only point of intersection of the planes $\to r . \to a = P_{1}, \to r . \to b = P_{2}, \to r . \to c = P_{3}$ then

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are non – coplanar

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Solution

The correct options are
C
are non – coplanar

D

Let $\to r = λ_{1} (\to b \times \to c) + λ_{2} (\to c \times \to a) + λ_{3} (\to a \times \to b) \to r . \to a = λ_{1} [\to a \to b \to c] \Rightarrow P_{1} = λ_{1} [\to a \to b \to c] λ_{1} = \frac{P_{1}}{[\to a \to b \to c]} s i m i l i r l y λ_{2} \frac{P_{2}}{[\to a \to b \to c]}, λ_{3} \frac{P_{1}}{[\to a \to b \to c]}$

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Similar questions

Q. Let

\to r

be the only point of intersection of the planes

\to r . \to a = P_{1} . \to r . \to b = P_{2} . \to r . \to c = P_{3}

then

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?

\to a, \to b, \to c

are non coplanar vectors and

\to p, \to q, \to r

are defined as

\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}]}

, then

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

is equal to

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

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Let →r be the only point of intersection of the planes →r.→a=P1,→r.→b=P2,→r.→c=P3 then

The correct options are C are non – coplanar D Let →r=λ1(→b×→c)+λ2(→c×→a)+λ3(→a×→b)→r.→a=λ1[→a→b→c]⇒P1=λ1[→a→b→c]λ1=P1[→a→b→c] similirly λ2 P2[→a→b→c], λ3 P1[→a→b→c]

Let $\to r$ be the only point of intersection of the planes $\to r . \to a = P_{1}, \to r . \to b = P_{2}, \to r . \to c = P_{3}$ then