Examine whether following vectors are coplanar or not- a- - b- - 2 c- - a- - 3 b- - c- and 2 a- - b- - c- -

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Condition for Coplanarity of Four Points

Examine wheth...

Question

Examine whether following vectors are coplanar or not. $\to a + \to b - 2 \to c, \to a - 3 \to b + \to c$ and $2 \to a - \to b - \to c$ .

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\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 a - \to b + \to c, \to b + \to c - \to a, \to c + \to a + \to b, 2 \to a - 3 \to b + 4 \to c .

2 \to a + 3 \to b - \to c, \to a - 2 \to b + 3 \to c, 3 \to a + 4 \to b - 2 \to c a n d \to a - 6 \to b + 6 \to c

\to a, \to b a n d \to c

\to a, \to b, \to c

_{1} = \to a - \to b + \to c,_{2} = \to b + \to c - \to a,_{3} = \to c + \to a + \to b

\to r = 2 \to a - 3 \to b + 4 \to c

\to r = λ_{1}_{1} + λ_{2}_{2} + λ_{3}_{3}

\to a, \to b, \to c

_{1} = \to a - \to b + \to c,_{2} = \to b + \to c - \to a

_{3} = \to c + \to a + \to b, \to r = 2 \to a - 3 \to b + 4 \to c

\to r = λ_{1}_{1} + λ_{2}_{2} + λ_{3}_{3}

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