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Condition for Coplanarity of Four Points

a⃗-2b⃗+3c⃗;2a...

Question

$\to a - 2 \to b + 3 \to c; 2 \to a + 3 \to b$ & $- 7 \to b + 10 \to c z$ Show that the points are notcolinear.

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Solution

$\begin{matrix} G i v e n, - - \to O A = ¯ ¯ ¯ a - 2 ¯ ¯ b + 3 ¯ ¯ c - - \to O B = ¯ ¯¯¯¯ ¯ 2 a + 3 ¯ ¯ b - - \to O C = - 7 ¯ ¯ b + 10 ¯ ¯ c - - \to A B = - - \to O B - - - \to O A = (¯ ¯¯¯¯ ¯ 2 a + 3 ¯ ¯ b) - (¯ ¯ ¯ a - 2 ¯ ¯ b + 3 ¯ ¯ c) = ¯ ¯ ¯ a + 5 ¯ ¯ b - 3 ¯ ¯ c - - \to A C = - - \to O C - - - \to O A = (- 7 ¯ ¯ b + 10 ¯ ¯ c) - (¯ ¯ ¯ a - 2 ¯ ¯ b + 3 ¯ ¯ c) = - 5 ¯ ¯ b + 10 ¯ ¯ c - ¯ ¯ ¯ a + 2 ¯ ¯ b - 3 ¯ ¯ c = - ¯ ¯ ¯ a - 5 ¯ ¯ b + 7 ¯ ¯ c t h e r e e x i s t s n o . λ, s u c h t h a t - - \to A B = - - \to A C ∴ p o i n t s a r e n o t c o l l i n e a r \end{matrix}$

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Q. If the position vectors of three points are

\to a - 2 \to b + 3 \to c, 2 \to a + 3 \to b + 4 \to c, - 7 \to b + 10 \to c

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Condition for Coplanarity of Four Points

Standard XII Mathematics

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